Reviews (2)

New view on Classical Electrodynamics
The differential geometric method has been one of the most
fundamental tools for theoretical physicists since its first
introduction into special relativity (general relativity) by Albert
Einstein in 1905 (1915). Later it has been applied to many research
areas, such as fluid mechanics, elastomechanics, thermodynamics, solid
state physics, optics, electromagnetism, quantum field theory, etc.

As a distinctive feature of traditional classical electrodynamics,
this book rests on the metric-free integral formulation of the
conservation laws of electrodynamics as represented by exterior
differential forms. Therefore the book will be of great interest to
graduate students and researchers in mathematics and theoretical
physics who work in field theory and general relativity.

The book consists of five parts; a short list of references and an
author and a subject index are included.Every part ends with a list
of references.The authors begin in Part A, as an introductory
section, with an elementary presentation of exterior differential
forms.The necessary geometric concepts, needed to formulate
classical electrodynamics and gravitational theory in the language of
differential forms, are explained in Part A and in Part C, too.The
axioms of classical electrodynamics, the integral formulations of
electric charge and magnetic flux conservation, are presented in Part
B. Subsequently, the linear connection and the metric are introduced
in Part C.The general framework is completed in Part D by a specific
electrodynamic spacetime relation and in Part E by applying
electrodynamics to moving continua and to rotating and accelerating
observers, for instance.

Moreover, a computer algebra program is introduced in the book in
a simple way, and some cartoon drawings will add to the tedious
mathematics some humor.As to the exposition of the book, we are
impressed by illustrations and diagrams, which support our geometrical
insight. The mathematical abstraction and physical relevance are
displayed neatly and appropriately.It is concise and comprehensive
as an introductory textbook for graduate students and a complete
reference book for researchers.

Thus, there is no doubt that many specialists will be interested
in the book under review.The book proves to be a good scientific
resource for university libraries as well as for graduate students and
researchers working in mathematical physics, field theory, and general
relativity.

Reviews (3)

A powerful mathematical language for physics and engineering
This is a well-written book on a very interesting and important subject: geometric algebra (GA) is a powerful and elegant mathematical language -- based on the works of Hamilton, Grassmann and Clifford -- that is especially well-suited for spacetime physics and several fields of engineering.

The authors adopt David Hestenes' viewpoint of a graded GA as a unified mathematical language that is coordinate-free, thereby stressing the fundamental role of geometric invariants in physics.

In fact, the elementary vector analysis -- which pervades almost all undergraduate (and even) graduate approaches to electrodynamics -- finds its roots in the misguided Gibbsian approach: Gibbs advocated abandoning Hamilton's quaternions and just work with scalar and cross products of vectors. However, the cross product has a major flaw: it only exists in three (or seven) dimensions -- if we require that (i) it should have just two factors, (ii) to be orthogonal to the factors, and (iii) to have length equal to the corresponding parallelogram.

Electrodynamics and relativistic physics, particularly, are elegantly presented through GA and otherwise cumbersome calculations may be circumvented in a simple and insightful way.

Mainstream physics and engineering cannot overlook GA anymore.

Compared to what ?
This is truly a great book for any one who is interested in not just physics, but physical reality. Although the ideas expressed therein have a long history and are by no means as uniquely those of its authors as were Albert Einstein's in his day, I believe that they will have comparable lasting value. Moreover the synthesis presented in this book, which builds pre-eminently on the work of Hestenes, is absolutely superb. Interested readers need not take my word for these claims, but are invited to prove it to themselves.

Although the above should be a sufficient review, my experience nevertheless indicates that it is a good idea to warn potentially enthusiastic readers against several common semantic misconceptions, lest they jump to conclusions which prevent them from ever taking that vital first step. Thus let it be clearly understood that Geometric Algebra is NOT:
(1) A replacement for linear/matrix/tensor algebra (on the contrary, it is a very nice complement to these formalisms).
(2) Identical, or even very close, to Emil Artin's earlier excellent book on bilinear forms with the title "Geometric Algebra".
(3) Another name for the enormous field "algebraic geometry" (it is indeed appropriate that the word stemming from "geometry" comes first in "geometric algebra").
(4) Just another reformulation of complex / quaternion / octonian analysis; for it connects all these purely algebraic objects, and many generalizations thereof, to Felix Klein's Erlangen Programme and Sophus Lie's theory of continuous groups.
(5) The ultimate theory of everything (although it probably will eventually be found to have something to do with it).

Geometric algebra IS a practical and natural (canonical) tool for formulating physical and mathematical problems in homogeneous spaces in a fully covariant fashion. But more importantly, you do not need to understand all those words in order to benefit from it, and this book is an excellent place for physicists of all stripes to start.

Articulate Path to the Future
The quality and importance of this book could hardly be overstated.Geometric algebra might casually be considered the "correct" generalization of linear algebra.By considering, for a start, directed line segments, the linear algebra courses presently taught in some high schools and all universities achieve miracles.Although viewed by a few of the slower students as merely unpleasant bookkeeping systems, linear algebra derives its power from allowing algebraic manipulation of sophisticated aggregate objects, namely vectors.The benefits are not just computational, but stem more importantly from a more powerful and more unified, although slightly more abstract point of view than a student had before studying.Geometric algebra is all that and much more.By extending consideration from directed line segments to the inclusion of direct plane segments, directed elements of three space, etc., an extremely flexible and elegant mathematical tool arises.It allows a deeper, quicker, and more concise treatment of essentially all of modern differential geometry.Its applications throughout physics are at once simplifications of ordinary matrix treatments and occasions to allow much greater insight.

Geometric algebra is a great theory, one of highest importance.It will, undoubtedly, find a dominant place in our mathematics curriculum at the highest speed allowed by our educational systems (the highest speed being actually quite slow).This book is an especially good place to begin study.It starts from the most elementary principles, and exposes the material with very thoughtful, clear presentation.The economy and elegance of the geometric algebra itself allows this one substantial but not enormous book to reveal great insights into many branches of study, from differential geometry and its applications to gravity theory to quantum mechanics and classical mechanics.

Reviews (3)

Great for physicists, okay for others
This is a great introduction to the Geometric (Clifford) Algebra.It'sfundamentally a physics textbook, however.Those readers whose only desireis to learn the Geometric Algebra might feel some frustration at having toseparate out the Geometric Algebra from the physics.Readers that preferlearning by exploring applications and examples will like this book; thosethat prefer explanations in the abstract will still enjoy many sections,but will have to make it through the more applied sections to get the fullstory.

Reading the book and working through the problems gives a firmgrounding in the use of the Geometric Algebra and teaches classicalmechanics besides.I could easily recommend this book as a physicstextbook on its merits in that area alone.

Excellent place to start learning Clifford Algebra.
A briliantly pedagogical introduction to Clifford Algebra as a unifiedalgebraic language for Newtonian Mechanics in three dimensions. The book isfull of applications and nonstandard approaches which simply cannot befound anywhere else. This is essential reading for anyone interested inClifford Algebras or who wants a deeper appreciation for classicalmechanics. This is a lot of book...

Reviews (1)

a marriage of geometry and algebra made in heaven
In 1990, I came across Hestenes' book New Foundations for Classical Mechanics in a university bookstore, and immediately purchased it. In 1999, I finally purchased the paperback version of CA to GC (Kluwer, please keep the paperback in print!).An engineer by training, I was previously only familiar with college vector analysis and with indicial tensor notation.These two books revolutionized my understanding of the algebraic representation of geometric information.Amazon.com now has the "look inside" feature in place for this book, so you can check the table of contents.

Science proceeds both by discovery and by a process of recasting what has been learned in simpler and clearer form.It is the fruits of this latter process that are presented in CA to GC, though some new mathematical results are also introduced.The authors have succeeded admirably in recasting large areas of intermediate to advanced mathematics in a powerful unified algebraic language of exceptional clarity.The authors show how the traditional languages of complex numbers, quaternions, matrices, vectors, tensors, spinors and differential forms are all subsumed by the elegant language of Clifford algebra, and their calculi by Clifford analysis.Quite apart from the pleasure that the clarity of Clifford algebra/analysis affords, its value also lies in making it easier to understand what has already been discovered, and thus extending the mathematical grasp of the human mind.I have often seen the terms "breakthrough" and "groundbreaking" applied to paltry advances in science, mostly by the innovators themselves, but surely Clifford algebra/analysis is deserving of such an appellation.It has been long in gestation, but its time has come.

Reviews (3)

For the Physicist - Not the Mathematician
Lounesto's book is replete with geometric and physical applications. The treatment is informal and non-rigorous and appears to have been designed with developing intuition in the reader. The text starts slowly working through many examples of particular Clifford algebras of interest and their relevence to physical problems. Towards the end Lounesto investigates general Clifford algebras and their associated spin groups as well as some specialized topics.

This is a good introductory text but fails to give the reader a firm mathematical basis of the material. Most striking is the almost total lack of proofs of any kind - the author is content merely to state the most important results but seldom leaves the reader with any mathematical justification. As such it is really a primer and the student of Clifford algebras must after working through the material move beyond to a rigorous algebraic text.

Lounesto's Clifford Algebras and Spinors
Clifford algebras make geometry and its applications to advanced physics incredibly simple, and this book is one of the best that I have read on this topic and on spinors.Readers outside physics should also study this book, if necessary with the help of a consultant or tutor to translate intomore or less ordinary English, because most fields of science or industryare in need of tremendous simplification.Lounesto's approach isalgebraic, as is Okubo's (see my review of his book) and Chisholm's(likewise), and Cambridge University Press as usual is at the head of thefield in publishing the deepest and yet most simple topics.Spinors (theword comes from spin plus the ending -ors) describe spin in quantum theory,and Lounesto has the most detailed division of the types of spinors that Ihave seen in a book together with their physical applications.Weyl andMajorana spinors describe the neutrino (of the weak force, although theformer only describe massless neutrinos), flagpole spinors appear todescribe the strong nuclear force/interaction and appear to be related toquark confinement, Dirac spinors describe the electron (Weyl and Majoranaspinors, unlike Dirac spinors, are singular with a light-likepole/current).Penrose flags (see my reviews of Roger Penrose's books) arerelated to Weyl and Majorana spinors.Penrose has an interesting theory oftwistors which is well reviewed in some of the popular science books.

Reviews (83)

One size doesn't fit all
First, on the question of whether the original lectures were a failure. In the April 2005 issue of Physics Today, Matthew Sands writes about the project that resulted in the Feynman Lectures. He disputes the claim that the undergraduates drifted away from Feynman's lectures in large numbers, and explains how Feynman's preface came about, and why he (Sands) finds it unduly negative.

It has always been widely agreed that the Lectures are insufficient as a standalone textbook, and best used as supplemental reading. As can be seen from the reviews here, Feynman's approach appeals to many readers, but falls flat with others. This is not surprising, as different people respond to different ways of explaining physics. As an historical aside, Feynman and Schwinger took such different approaches to developing quantum electrodynamics theory that it wasn't immediately clear that their formulations were even equivalent. Most physicists find Feynman's approach easier to learn, but others find it unsatisfying. People are different. Physicists are different. Even physics students are different. There is not, and will never be, one book that is the best for every reader. The Feynman Lectures are great because they have been so enlightening to so many people, not because they meet the impossible standard of being clear to every reader.

Very informal but entertaining
I read these books several years ago because one of my professor is a super Feynman fan.He told us how wonderful these lectures are.By curiosity,I found them out in the library and tried to read them.I must say that these books are not that easy to read.The style is very informal.There are not many equations in the books.If you don't have some knowledge about a topic and you want to learn it from these lectures,you will soon feel very frustrated.I agree that Feynman is a great physicist but probably he is not that good at preaching knowledge.If you ever read Freeman Dyson's Disturbing the Universe,you ought to know that Feynman is not very good at explaining his own ideas at least in those period of time while Dyson was in Cornell.I shall not suggest a beginner starts learning physics from these lectures.But if you have learned physics several years and want to see some fresh explanation of some topics you are familiar with,you can find many interesting stuff in these lectures.I think that the true value of these books.

Reviews (10)

Good stuff badly written
I'm going to mention the second volume almost exclusively.This is where the action is located.It is hard to find any equivalent treatment of circuit theory using algebraic topology. You should have some mathematics background or some patience and a stack of books on algebra and algebraic topology so you can understand what these authors write so poorly.However, while the text (vol.2) loses a star for being horribly written, it gains four stars for the amazing content.If you are patient you will see a side of circuits you have never dreamt of and then you will be led into the generalized (continuous)version which is electromagnetics.

If you are looking for some really accessible and really interesting mathematics on circuits and EM buy this book (or buy it used, I bought my hardcover for 10$) You might also find it useful to consult the appendix in Frankel's Geometry of Physics for comparison.

Have fun and keep in mind that the book is written by sadists, clever and intelligent, but sadists all the way!

Simply fascinating!
In short, I find this kind of a book very rare indeed.

If you are doing physics and electronics at the undergraduate level, this book will open your eyes to a whole new unified approach to several on-the-surface different topics. I wonder why many course designer's haven't looked at this book and realized how accessible it has made some of the relatively modern concepts. The authors laudably attend on each concept with a passion to make the reader confident of grasping at least a few different ways of looking at it, keeping the core well in view all the time. It is also to their credit to have kept the beauty in the ideas intact with a good balance of abstraction and concrete instances.

In particular, the authors treatment of exterior calculus is an eye opener if you are new to the topic. For a student only exposed to traditional methods, it is a revealer to see the laws of linear electrical circuits as well as Maxwell's equations of electromagnetism being expressed in precisely the same language. It is totally to the credit of the authors to have presented the concepts in such a simple to understand progression. For example, they make you see clearly why you have understood the divergence theorem or Stokes theorem of conventional vector calculus if you've grasped the essence of the calculus of functions of a single variable. Its a fantastic voyage folks, and you've got some of the best guides methinks.

All those who find physics and mathematics a drag at college should grab this book and be enlightened. I wish they fix some of the errors in the book in future editions, but the errors don't at all hinder the learning.

Ten thumbs up!

Reviews (8)

satisfactory physics, insufficient/informal mathematics
I took the graduate course on general relativity from Professor Carroll and therefore had a first hand exposure of how this book is used in teaching and received a satisfactory grade from the course, which may or may not be relevant for the value of my review, if there is any.

The book by Sean Carroll on general relativity gives an exposition of the foundations of classical field theory of gravitation, presents the elementary solutions and some further applications to (the sexy subject of) black holes and cosmology with an emphasis of symmetries. A chapter on string theory is also included. The quality of printing is more than good, the chapters and their organization, other than the first, should be typical of a textbook on the subject. My major criticism is more on the style of writing than the content.

Many people believe that the hardship they would encounter during their training in Einstein's general theory of relativity is the excessive presence ofmathematics or more precisely differential geometry in the textbook presentations of this truly amazing branch of physics. This is a false conviction because of two reasons. It is false to think mathematics is difficult, for mathematics (and therefore differential geometry) is not difficult. How can it be?- it is logical! More importantly and more to the point there is not enough of mathematics and/or mathematical rigor in the textbook writing these days. Physicists (and chemists) of our time arrogantly and ignorantly use the science fiction in lieu of science, such as the atrocious object called (Dirac's) delta function which is not a function at all orthe joke of infinite matrices in quantum theory which is not the proper way to do business. Like many others, the plague of non science, the delta "function", is present in Carroll's treatise. Again those in the field of physical sciences postulate, reflect, and sometimes even solve an equation without any worry on the existence of solutions! A stunning case is the following: The proof that the quantum mechanical Coulomb material (atoms, molecules, solids) is indeed stable, which means its energy spectrum has a lower bound, is provided by Lieb long after this theory was applied to spectroscopy, solids, etc. To make the sensation more spectacular I must say to this day not many "scientists" care about it! OK, I understand, Einstein's equations are hard or in general impossible to solve with known techniques but it would have been philosophically adequate to include an existence proof (or a conjecture thereof) pertaining to the solutions which you cannot find in the book. It is not a bad habit to wonder when the solutions might not exist!

I found it disrespectful when I read the remark about the brace-notation of the Christoffel symbol of the second kind as "funny". Not that I have a problem with Princeton School's \Gamma notation, after all why not?- they are equivalent and \Gamma is more convenient, but I believe that was the notation used by the disciples of the old school, therefore I suggest the more positive adjective "authentic". This example typifies (Am I just?) the informal writing style that can be experienced by the reader. Perhaps a manifestation of the decadence of our age or perhaps not, this writing style, by no means specific to Professor Carroll but an epidemic, is something that I am growing uncomfortable. It is a shock when one compares it with say Euclid, Archimedes, Euler, or Kolmogorov. They are never boring and yet they are seductively formal.

I must apologize because of an apparent hypocrisy between this review and my other mediocre praises of the works of Landau or Dirac that can be found on this web site. If this work is negatively criticized, one must do the same for Dirac's lecture notes on relativity. However, in those days I didn't know the writings of Clifford Truesdell nor I was aware of the research and findings of Eliot Lieb which are the causes of my disillusionment.

good math chapters, not at beginner's level after that

I had a course based on that book and I've read chapters 1-6 (out of 9 chapters total) plus all the appendices. Also, I've solved some of the problems.

Please keep in mind my review is from a beginner point of veiw. Readers more experienced in GR may feel different but that book is supposedly written for beginners right?

The math chapters 2 and 3 are worth reading because they will teach you tensor analysis on manifolds in much clearer way than other books. The book makes a clear distinction between assumptions, choices (like working with a metric compatible connection), or derived facts. It is nice that the book makes a difference between a Christoffel connection and a generic connection. The appendices are worth reading too cause they will give you a feeling for some new to you math necessary for GR like pullbacks, Lie Derivatives, hypersurfaces etc.

Chapter 4 is worth reading too cause it makes clear that Einstein's equations are just the simplest guess out of many other possibilities. Also it shows how we generalize physical laws from special relativity to GR making it clear our choices are the simplest ones but not the only ones possible.

The chapters after that discuss applications of GR like black holes, gravitational radiation, cosmology etc. Of these, I've read only the black holes chapters 5 and 6 and I wasn't able to understand 100% what was goin on. The problem was that the book uses concepts that you still don't quite understand if you are a beginner like 'spacelike singularity' or 'conformal diagrams'. That is informative but the book doesn't provide the necessary level of detail and examples for beginners so you could really master such concepts and use them in your practise.

There are problems after each chapter but not the necessary beginners problems that increase your conceptual understanding of the theory. Instead, some of the problems are just tedious algebra of type 'find the curvature for some general form of the metric' for which specialists in the field use symbolic programs like Mathematica. Solving these by hand proves that you can take derivatives and you are a mazochist but not that you understand GR. Other problems are really relevant to your education but are not dirrectly connected to the discussion in the text. Because of that you have to solve them from scratch and it will take you ages ...

If you are a beginner like me, you should read the math chapters and all appendices of Carroll's book plus chapter 4. Then you should read a real book for beginners with a lot of examples how to apply GR in real calculations and how to understand it. For that I recommend James Hartle's "Gravity: An Introduction to Einstein's General Relativity" and Bernard Schutz's "A first course in General Relativity". After that hopefully you will understand the rest of Carroll's book better. My experience was that often I had to read Hartle's book in order to understand and solve a problem in Carroll's book.

Reviews (32)

good reference for advanced, NOT A LOGICAL INTRO to GR

This book is known as the 'bible' of General Relativity or 'MTW'.

People with different preparation will perceive MTW in different ways:

The beginners in GR very often will feel that the book is a good reference and shows 'properties' of the defined objects instead of explaining the logical necessity of demanding such properties. My first course in GR was based on that book and although I learned some 'index gymnastics' from it, very often I had questions of the type 'where does this come from, why is it defined this way'. Often I would read about something like 'affine parameter' and I would not understand its importance at all.

For beginners I recommend the books from J.Hartle, B. Schutz, and S. Carroll in order of increasing abstraction. I am currently in the middle of course based on the Carroll's book and I understand things I have never ever been able to understand from the 'bible' like the fact that we may define different connections but only one of them is metric compatible and we CHOOSE to work with it, or that we CHOOSE to work with a torsion free connection, or that reparametrizing a geodesic may not give you back a geodesic (in relation to the affine parameter remark above) ... Such facts are either not clearly spelled in the 'bible' or they are digged in somewhere 300 pages away ...

Once you are past your first (or better second) course in GR, that book will be an invaluable reference for you with plenty of examples how to apply different computational and theoretical techniques in GR.

The reviewers that give it high rating are obviously either experienced in the field or are begginners that value a book only because of the well-known authours.

The book is really a titanic effort to compile all relevant pieces of info into one thick volume BUT PLEASE PLEASE think carefully before you recommend it for INTRODUCTION to General Relativity !!!

Gravity Defying
After reading this text, I became thoroughly competent in General Relativity as well as the requisite elegent mathematical tools needed to fully understand this truly beautiful subject.Moreover, I have since gone further in this field with my own self-discovery.In particular, in my search for a unified quantum field theory of gravity, I have discovered that a new field emerges out of the space-time energy manifold, which gives rise to a gravity-induced collpase of the wave function of a system.This emergent field is self-referential and emergent and is the basis of consciousness.Upon fully realizing the implications of this newly discovered theory, I knew that I should be able to locally vary the space-time energy manifold around me by mere thought alone.Indeed I did this on the night of November 14, 2004 and levitated a good meter off the ground for at least a full minute before my stupid girlfriend came into the room and shouted "Devil!You're a devil!" and fled in horror.My concentration was instantly broken and I fell to the ground, spraining my ankle in the process.Damn gravity!And come to think of it, this is all the fault of Wheeler, Misner, and that Californian hippie dude guy, Kip Thorn.Stupid gravity book!Yeah, it's brilliantly written and a fascinating subject.But now I have a sprained ankle and my girlfriend left me and won't talk to me.I just might sue all these authors for pain and suffering.All my girlfriend does now is send me some religious tracks and tells me that she and her prayer group partners are praying for me.I keep telling them this isn't supernatural and that it is all science, but they hold up and cross their fingers at me in the makeshift form of a crucifix and quote bible verses at me.Stupid bible-quoting prayer group groupies!I'm not sure but I think they are a cult maybe.So no girlfriend now.I just might sue for emotional damages too!Anyway, I give this book five-stars if you too want to learn all about gravity.But be warned!You might start levitating one night, your girlfriend might get all freaked out, and then you fall to the ground and crash, both literally and figuratively, and just end up lonely and angry and everything.But you'll still be a master of GR and hey who needs that no good, easily scared, verse quoting girlfriend anyway?!Oh, I didn't mean that.Really Karen, if you're reading this, please baby, come back.I promise no more "devil flying tricks."OK?Oh yeah, this is definitely a great book--and probably won't really ruin your life.

Reviews (3)

The best introduction to Special Relativity (in English)
This textbook is, probably, the best introduction to special relativity in English language.

Professor Rindler presents a skilful introduction to flat spacetime using four-tensors and allowing the neophyte to get leisurely acquainted with the nondefinite metric of Minkowskian spacetime through several worked and insightful examples -- not to mention the most interesting collection of problems, presented at the end of each chapter, that I have encountered in a textbook at this introductory level.

Having said that, I must add two remarks.

My first remark is that I cannot understand the reason why textbooks in English (as this one) insist in deriving the Lorentz transformation using Einstein's second postulate on the speed of light: as already pointed out by Jean-Marc Levy-Leblond (Am. J. Phys., Vol. 44, pp. 271-277, 1976), this second postulate is not only superfluous but also epistemological misleading -- see, e.g., the French textbook by J. Hladik and M. Chrysos (Introduction a la Relativite Restreinte, Dunod, Paris, 2001) which can be bought at Amazon.fr.

My second remark is that I think Hestenes' geometric algebra -- see, e.g., his article in Am. J. Phys., Vol. 71, pp. 691-714, 2003 -- is the most appropriate mathematical tool to present special relativity, even at the undergraduate level. You can check this out in his book "New Foundations for Classical Mechanics" (2nd ed., Kluwer, 1999), namely in Chapter 9.

The Elegance of the Mathematics Revealed
Special Relativity is really nothing more than an application of linear algebra, but this book shows that upon reflection it becomes a particularly elegant application of linear algebra. I have never come across a book which makes this so obvious.

This book should be accessible to advanced undergraduates, those who have the level of mathematical sophistication required of your upper level undergraduate classes.

Isbn: 0486432351
Sales Rank: 179865
Subjects:  1. Advanced    2. General relativity (Physics)    3. Generalized spaces    4. Geometry - General    5. Mathematics    6. Relativity    7. Science/Mathematics    8. Mathematics / General   

Reviews (6)

good introduction
The language ofdifferential forms presented at the level of thisstudent-friendly text provides a refreshing outlook on vector analysis. Andwith a view towards more advanced courses, this book hints at the remarkable computational prowess it bears ondifferential geometry at large.

In light of the author's heuristic approach,the book does well in setting the stage for the applications he has in mind (casting Stokes' theorem in its true form,for example).

One should then go on to read books like Do Carmo, written in a similar vein,but this time,delineating the algebraic machinery needed to set up the theory in a more rigourous framework.

Have fun!

A good introduction to forms
Fortunately there are several books, at an introductory level suitable for undergraduate students, on how differential forms constitute a "new" powerful mathematical technique that surpasses the outdated vector calculus. This book by Steven H. Weintraub is a very good example among others -- such as: (i) "Advanced Calculus: A Differential Forms Approach" by Harold M. Edwards (Birkhäuser, Boston, 1994); (ii) "Vector Calculus, Linear Algebra, and Differential Forms" by John H. Hubbard and Barbara Burke Hubbard (Prentice Hall, NJ, 2nd ed., 2002).

As far as I know, it was in "Gravitation" -- by Charles W. Misner, Kip S. Thorne and John Archibald Wheeler (Freeman, San Francisco, 1973) -- that a pictorial representation of forms was clearly presented to physicists for the first time. These authors went even further, explaining how "forms illuminate electromagnetism, and electromagnetism illuminates forms" (p. 105).

However, until now, it seems that in engineering forms have been disregarded -- despite early attempts by George A.Deschamps (see, e.g., his paper "Electromagnetism and differential forms", Proc. IEEE, Vol. 69, pp. 676-679, 1981), not to mention Harley Flanders's book ("Differential Forms with Applications to the Physical Sciences", Dover, NY, 1989). Perhaps the book by Ismo V. Lindell ("Differential Forms in Electromagnetics", IEEE Press/Wiley, NJ, 2004) will be able to change this sad scenario.

It seems that the difficulty lies mainly in the fact that a proper understanding of k-forms, as antisymmetric (0,k) tensors in differentiable manifolds, requires the study of technical demanding subjects such as de Rham cohomology. However, this book shows that it is possible to make an introduction to forms without mastering such concepts in topological and smooth manifolds -- although there is an extensive bibliography on this subject out there (the books by John M. Lee on manifolds are my favorite).

For more advanced readers, the book by Friedrich H. Hehl and Yuri N. Obukhov on the "Foundations of Classical Electrodynamics" (Birkhäuser, Boston, 2003) is, in my opinion, the most elegant exposition on the relation between electromagnetism and forms.

Isbn: 0195146654
Sales Rank: 531493
Subjects:  1. Electricity    2. Electricity And Magnetism    3. Electrodynamics    4. Electromagnetism    5. Physics    6. Science    7. Science/Mathematics    8. Electricity, magnetism & electromagnetism   

Isbn: 0471648019
Sales Rank: 946837
Subjects:  1. Applied Electromagnetics    2. Differential Equations    3. Differential forms    4. Electromagnetism    5. Engineering - Electrical & Electronic    6. Mathematics    7. Science    8. Science/Mathematics    9. Technology & Industrial Arts    10. Electricity, magnetism & electromagnetism    11. Electronics & Communications Engineering    12. Science / Electromagnetism   

Reviews (17)

A classic text
Yes.The writing is clear and concise.The book is packed with information.

This book is for those who want to do physics, and it teaches one to do physics the way physicists do it.It is the second volume in L&L's Course on Theoretical Physics;it follows the volume on Mechanics.And the next logical topic is relativity.So this book starts out with special relativity, four-vectors, relativistic mechanics, and particle decay and scattering.

But then we proceed to what I think really needs to come next, namely a discussion of electromagnetic fields.We derive Maxwell's equations.We learn a little about optics.And then we get to the field of moving charges, and radiation of electromagnetic waves.These are very important topics.If I were teaching a class on relativity, I'd make good use of these two chapters.I think it is very instructive to learn about the field of an accelerating charge.

The sections on general relativity are especially well written.And we learn how to work all sorts of general relativity problems, such as finding the radiated energy and angular momentum loss for a system of two bodies moving in elliptical orbits.The icing on the cake is a short chapter on cosmology.

This is the way to learn physics.

Amazingly lucid
I expected this book to be dense and incomprehensible, like I have found other of their books before, but the material is actually clearly presented, and not as terse as it may seem from a first glance. While not as comprehensive in coverage as Jackson's Classical Electrodynamics, I find it easier to follow. As far as coverage of GR goes, it's succinct: I found it very helpful to work through this book before tackling MTW.

Reviews (66)

Great book, but certainly not for the timid...
This book will challenge your scholastic aptitude. My prof who taught me this book solved ALL the problems when he was a graduate student at Stanford. He went to Caltech when he was 16 and is also the inventor of the free electron laser. You don't have to be smart like him, but get ready to really push yourself. Or else, you won't survive.

The book for electrodynamics
A legend in its field; precise, vast, clear and once u can handle the math needed very rewarding. Simply a must for a physicist, reguardless the field. Furthermore a nice book for the eye and well made, so you wont have issues of this book falling appart in ur arms after a few openings.

Reviews (5)

Good Introductory Text.
Not many books on gravitation are clear and concise but this one is.
I have the big Bible "Gravitation" from Wheeler but then if you are
using for introductory course then this one is the best. It assumes that reader is new to this subject and proceeds step by step. Tensors are introduced as they are needed in the text so that you don't get lot of information at once. The chapters are as follows,

1: Gravitational Physics
2: Space, Time, and Gravity in Nwt physics.
3: Principles of SR.
4: SR Mechanics
5: Gravity as Geometry.
6: The Description of Spacetime.
7: Geodesics
8: The Geometry Outside a Spherical Star.
9: Solar System Test of GR
10: Relativistic Gravity in Action.
11: Gravitational Collasp and Black Holes.
12: Astrophysical Black Holes.
13: A Little Rotation.
14: Rotating Black Holes.
15: Gravitational Waves.
16: The Universe Observed.
17: Which Universe and Why?
18: A Little more Math.
19: Curvature and Einstein Equation.
20: The Source of Curvature.
21: Gravitational Wave Emmision.
22: Relativistic Stars.

I guess it's a very good text for the introduction to GR. Less math than Weinberg but precisely good. If you are considering an intro to GR, Gravitation then this would be a good choice. The price is also very reasonable.

Graduate Student Review of Gravity by Hartle
Great introduction to Relativity. Many examples and relations to the 'real world'. Similar approach as The Bible (Misner, Thorne, and Wheeler), but, in my opinion, this book is much more organized and reads easier.

Reviews (5)

Very Good
This book is for all those who want to understand more about quantum mechanics. It explains in a very intelligent way the essential differences between a classical theory and a quantum mechanical one. Highly recommended. You will not learn from this book on how to solve e.g. scattering problems, this book focuses on understanding the theory rather than applying it. I enjoyed it very much.

Not that easy, but ...
I appreciate the author's approach as much as the other, "five star" reviews.Isham has tackled some very difficult material and consistently gone to the heart of the problems involved with the meaning of quantum theory.He has treated the many different approaches - from pure pragmatism to hidden variables and many worlds - with fairness and due respect for each.My only disagreement with the other reviewers is their assessment of the book's accessibility.The mathematics is heavy on abstractions.As a former graduate student in physics (admittedly long ago), I found it rougher going than I expected and spaced out several of the final subjects such as quantum logic.Nevertheless I came away with a better understanding of the foundations of quantum mechanics, and I have no regrets over buying the book.

Reviews (11)

Good
I used this text for a course after taking an undergraduate GR course based on Shutz.I found Shutz to be a much clearer and pedagogical text, and don't think I would have learned GR as easily if I had started with Wald.I think one requires greater mathematical preparation than I possess to fully appreciate the discussions involving topology in the second chapter and appendix.Oddly, however, this text becomes clearer as the reader advances through it:later chapters were more straightforward and still concise.

Valuable
A valuable reference for GR. If one has to learn something on GR for the first time, then this is probably not the best book to start with (even if the first part on GR, chapters 1-6, is quite clear). On the other hand the book contains a very good treatment of Energy in GR, Killing fields, and ADM Energy-momentum. This is in brief a great buy, if one does not feel fine facing Hawking-Ellis.

Reviews (6)

Know your Differential Geomery & Tensor Calculus beforehand.
If an exposition is what you're looking for - this is not it, some great less technical books exist, like Kip Thorne's "Black Holes and Time Warps..", also, the short outline of differential geometry is there more to get the reader acquainted with use of terms in the book and not as a tutorial.
Knowledge of tensor calculus - inside out, is not an option, personally I found Misner, Thorne and Wheeler's (classic) "Gravity" a lot better.
The true strength of this book though, is the clear and concise way of introducing concepts, built empirically, you really get the feeling these guys know what they re talking about.
I had some problems with this text though, its hard to completely get the context of which a some objects described - or even why they are there in the first place (unless you've already been a GR physicist for the last 30 years..), the prerequisites are demanding, it's absolutely impossible to follow through without seriously spending your entire days trying to figure this stuff out, in this aspect it is NOT a self study book and requires an ability to talk to a professor or a graduate student that can help clear things up for you (something I had to do several times).
Conclusion, not a bad text book - if you're already fluent on the technical aspects.
Enjoy.

The Large Scale structure of good science books (& spacetime
I think that this book has great depth, and is one of the best Stephen Hawking books I have read.My favourite remains 'A Brief History of Time', but still this book is extremely excellent.My compliments to the chef.

A classic in mathematical general relativity
This book is now a classic and is written by two giants in mathematics and physics. It wil be used for many years to come and is certainly one of the most widely quoted in the subject.

The authors begin the book by a discussion of the role of gravity in physics and its role as determining the causal structure of the universe. They introduce the idea of a closed trapped surface, setting the stage for the goal of the book, namely the study of the conditions under which a space-time singularity must occur. Black holes and the beginning of the universe are cited as examples of these singularities. The authors also outline briefly the content of each chapter. A neat argument is given for the significance of focal points via the use of Raychaudhari's equation.

The second chapter is an overview of the background in differential geometry needed in the rest of the book. Although complete from an axiomatic point of view, the approach is much too formal for readers who do not have a knowledge of differential geometry. Such a reader should gain the necessary background elsewhere.

General relativity as a theory of gravitation is discussed in chapter 3. Spacetime is assumed to be a connected 4-dimensional smoothmanifold on which is defined a Lorentz metric. The topologyis assumed to be Hausdorff. Some of the more interesting or well-written parts of this chapter include the example of a spacetime that is not inextendible, the determination of the conformal factor for the spacetime metric, and the discussion of alternative field equations.

The authors discuss the physicial significance of curvature in chapter 4, namely its effect on families of timelike and null curves. The most important part of this chapter is the discussion on certain inequalities tht the energy-momentum tensor should satisfy from a physical viewpoint. These inequalities, called the weak energy condition and the dominant energy condition, allow the authors to prove the existence of singularities ina later chapter. The reader can see clearly the role of the Jacobi equation, and its solution, the Jacobi field, in measuring the separation of nearby geodesics. The existence of conjugate points is proven, and shown to imply the existence of self-intersections in families of geodesics. As a warm-up to showing the non-existence of geodesics of maximal length, the authors employ variational calculus to study how to vary non-spacelike curves connecting points in convex normal neighborhoods in spacetime, and between points and hypersurfaces. In particular, it is shown that a timelike geodesic curve from a hypersurface to a point is maximal iff there is no conjugate point to the hypersurface along the curve. In addition, the authors prove that two points joined by a non-spacelike curve which is not a null geodesic can be joined by a timelike curve.

The authors consider the exact solutions of the Einstein field equations in chapter 5. Most of the "usual" spacetimes are considered, including Minkowski, De Sitter, Anti-de-Sitter, Robertson-Walker, Schwarzschild, Reissner-Nordstrom, Kerr, Taub-Nut, and Godel. The emphasis in on the global properties of the spacetimes and the existence of singularities in them. The famous Penrose diagrams are used to "compactify" spacetimes in order to study their behavior at infinity and their conformal properties. The authors first introduce the concept of a future (past) Cauchy development here, so important in later developments in the book. The reader can see the tools developed in chapter 4 in play here; for example, the existence of a singularity in a spatially homogeneous cosmology is shown to follow directly from the Raychaudhuri equation. The existence of the singularity is proved to be independent of any acceleration or rotation of matter in such cosmologies.

In chapter 5, the authors consider the causal structure of spacetime, namely the study of its conformal geometry. The consideration of the set of all metrics conformal to the physical metric allows one to discuss "geodesic completeness" of spacetime, this concept forming the basis of a later definition of a singularity in spacetime. The more interesting topics discussed in this chapter include the causality conditions (there are no closed non-spacelike curves), and the Alexandrov topology and its connection with the strong causality condition (every neighborhood of a point contains a neighborhood of the point no non-separable curve of which intersects it more than once). When strong causality does hold, the Alexandrov topology is equivalent to the usual manifold topology, and thus the topology of spacetime can be determined by the observation of causal relationships. The discussion on the role of global hyperbolicity in showing the existence of a maximal geodesic is also very well-written.

The next chapter is pretty much independent of the rest, and was put in no doubt for the mathematician who desires to understand the Einstein equations as a set of nonlinear second-order hyperbolic partial differential equations with initial data on a 3-dimensional manifold, the famous Cauchy problem in general relativity.