Spacetime and Geometry: An Introduction to General Relativity

Book Description

Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject. Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology. For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity.

Customer Reviews:

Wordy and Wonderful.......2006-12-12

This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner. With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity. This is very different from, and compliments nicely, the clarity and directness of Wald. As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book. Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.

Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.

Also, his chapter on cosmology is better than any I've seen.

BY FAR the best book on GR.......2006-10-21

I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is. Sure there is a lot of math in it however that also is very clearly explained. In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject. If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it. I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.

(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study. The prima donnas don't like Kay's book because it "doesn't have enough theory." I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)

Because, you can always skip through certain sections if the math is too heavy and go back through it later. And like I wrote earlier, you won't find a better introduction to the mathematical material than here.

Carroll should be given the Nobel prize for this book. If not in Physics, then in literature. I'd give this textbook 10 stars if I could.

A nice blend of the ideas of physics with mathematics.......2006-04-11

Kudos to Carroll.

This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.

Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.

This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.

I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.

Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.

Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.

He then presents some introductory GR material by applying the mathematics.

Great Book But Won't Get You To The Promised Land.......2005-12-14

My comments come with a few caveats.

1. This is my fourth GR book.
2. I'm not hardcore into physics. I'm not a physic grad and I'm reading GR for fun. I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.
3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.

With these caveats in mind, here are my comments.

First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness. Here is my full ranking of authors from my limited reading: 1. schutz 2. hartle 3. penrose 3. carroll 4. wald 5. physics journal articles

Second, using the rankings above, I recommend Carroll as the second port of entry. If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite. If you've had advanced calculus and geometry already, jump in with carroll (#3). But you'll be hard-pressed to find anyone else as polite to the reader. He won't prepare you for 80 percent of what's published. If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).

Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end. I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.

Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4). Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book.

good math chapters, not at beginner's level after that.......2005-03-07

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.

Relativity: An introduction to space-time physics

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An excellent introduction to Relativity

Relativity: An introduction to space-time physics
Steve Adams
Manufacturer: CRC
ProductGroup: Book
Binding: Paperback

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ASIN: 0748406212

Book Description

Provides the essential principles and results of special relativity as required by undergraduates. The text uses a geometric interpretation of space-time so that a general theory is seen as a natural extension of the special theory. Although most results are derived from first principles, complex and distracting mathematics is avoided and all mathematical steps and formulae are fully explained and interpreted, often with explanatory diagrams.; The emphasis throughout the text is on understanding the physics of relativity. The structure of the book is designed to allow students of different courses to choose their own route through the short self-contained sections in each chapter. The latter part of the book shows how Einstein's theory of gravity is central to unraveling fundamental questions of cosmology.

Customer Reviews:

An excellent introduction to Relativity.......2003-05-21

If you are a ambitious highshool student or a physics freshman this is the best place to get started on special realtivity.
It is far less mathematically demanding then many books out there and clear on physical concepts.
(ch.1) Good review of classical ideas.
(ch.2) Need for special relativity, good explanations of
galaian and lorentz transformation, and uses of the latter.
(ch.3) Good introductions to spacetime geometry (the invariant
interval) and relativistic mechanics.

(ch.4) Good introduction to basis of general relativity and cosmmology.

One of the great things about the book is that it takes the common 'popular' accounts one step further by intoducing physics in precise languge and formulas. So that you can apply your knowldege to actully solve some problems and gain further understanding. There are problems at end of each chapter and they are (mostly) supplemented by answers in an appendix.

One thing that is left out completely is relativistic electrodynamics, of course that's only sutibale for a more advanced book. I would've liked to see the power of four vectors utilized more and see the role of tensors.

Appearance and Reality: An Introduction to the Philosophy of Physics

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Excellent in its intended capacity as introduction...
very good up to page 140 then thumbs down

Appearance and Reality: An Introduction to the Philosophy of Physics
Peter Kosso
Manufacturer: Oxford University Press, USA
ProductGroup: Book
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ASIN: 0195115155

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Appearance and Reality: An Introduction to the Philosophy of Physics addresses quantum mechanics and relativity and their philosophical implications, focusing on whether these theories of modern physics can help us know nature as it really is, or only as it appears to us. The author clearly explains the foundational concepts and principles of both quantum mechanics and relativity and then uses them to argue that we can know more than mere appearances, and that we can know to some extent the way things really are. He argues that modern physics gives us reason to believe that we can know some things about the objective, real world, but he also acknowledges that we cannot know everything, which results in a position he calls "realistic realism." This book is not a survey of possible philosophical interpretations of modern physics, nor does it leap from a caricature of the physics to some wildly alarming metaphysics. Instead, it is careful with the physics and true to the evidence in arriving at its own realistic conclusions. It presents the physics without mathematics, and makes extensive use of diagrams and analogies to explain important ideas. Engaging and accessible, Appearance and Reality serves as an ideal introduction for anyone interested in the intersection of philosophy and physics, including students in philosophy of physics and philosophy of science courses.

Customer Reviews:

Excellent in its intended capacity as introduction..........2000-03-14

I would imagine that the factor pivotal to appreciation of this book is the reader's stage of understanding of the issues discussed within this book.

Particulaly impressive was the conciseness and clearness of the explanations of both relativity and quantum mechanics, two subjects that I would imagine can be notoriously difficult to deal with when ill explained. Aside from aformentioned technicalities regarding quantum physics, perhaps the author could may have spent more time considering the epistemological issue of the very validity of, in particurlar relativity, the 'foundations of modern physics discussed'. They seemed briefly considered, yet tossed aside it seems due to the author's attitude that the apparent current non-existence of what may eventually supercede the areas of physics in question. So, basically, the book was themed upon evaluating reality using the best tools we have at this moment to evaluate what constitutes it.

None the less, as an indication of the perspective physics can provide as to the very nature of reality and existence, this book can be invaluable.

very good up to page 140 then thumbs down.......1999-07-14

Good overview of the special and general theory of relativity as well as quantum mechanics. No equations are used and the author is able to demonstrate these ideas very well.

However the author bias becomes very clear as he explains Bell's theorem . The author points out that no local hidden variable theory can explain the results presented by quantum mechanics. He seems to miss the point that quantum mechanics is NONLOCAL with or without hidden variables . He clearly is in the copenhagen camp but stresses that popular publications on the subject are incorrect in concluding that everything is indeterminate, after all, things such as mass,charge etc. are determinate.

The author seems to accept "in stride" the nonlocality in the copenhagen interpetation and then uses nonlocality as the biggest argument against the deBroglie-Bohm pilot wave interpetation stating that it is a "blatant" violation of the special theory of relativity. Apparently the instant collapse of the second wave function when the first is measured in EPR is more realistic in his view. He then corrects himself and states that it is really not a violation of the special theory "empirically".

These kind of inconsistencies and contradictions are rampant after page 140. In the end the best critisism the author could level at the Bohm interpetation is that it is "epistimological anti realism"

Customer Reviews:

A Breakthrough in Undergraduate Texts.......2007-03-15

A book I really wouldn't have thought could have been written. There are a lot of books on general relativity at the superficial level, call these books 'mathless.' There are monumental tomes aimed at the graduate student level, call these books 'tensor calculus.' Here is a book exquisitely positioned between these others. The student will need to have had differential calculus, and perhaps a bit of basic physics, and with these he will get a pretty good, introductory understanding of General Relativity.

The real key to this book is that it explains a lot, but then it open up a bunch of other questions, questions that we really haven't answered yet -- things like dark matter, dark energy, accelerating expansion of the universe, and more.

The book ends with: 'How can physics live up to its true greatness except by a new revolution in outlook which dwarfs all past revolutions? And when it comes, will we not say to each other, Oh, how beautiful and simple it all is! How could we ever have missed it so long.'

That's just the awe, the vision, that we want new and budding physicists to have.

Good book if you like mathematics!.......2007-01-05

This is the best book about General relativity ( GR ) that I have ever read. Instead of trying to explain GR with words the author is using mathematics to to illustrate some of the consequences of GR. This means that some mathematical knowledge is required ( but not knowledge about tensors and dfferential forms ) and that the reader need to spend some time with paper and pencil to truly understand the text. The examples is concentrated on what is happening around black holes but the advance of Mercury's perihelion and the slowing of light around the Sun is also described. A very good book!

Amazing Introduction to a Very Esoteric Subject.......2006-06-11

Einstein's general theory of relativity is perhaps one of the most mathematically intense areas of research any physicist or astronomer could undertake. However this book takes the subject and turns it into a joyous romp through curved spacetime.

By avoiding the field equations and focusing on their solutions the authors impart to the eager student an overview of general relativity and set the stage for a more rigorous approach to be undertaken later. This book is the perfect introduction to the subject.

The book is well suited for advanced undergraduates who have had several hours of physics and mathematics. It is likewise suited to serve as a introductory text for graduate students that are studying astrophysics and astronomy. In the latter case the text serves well as an overview of what general relativity is, many of its findings, its predictions, and its relevance to observational astronomy.

If you have a basic understanding of calculus and have studied the special theory of relativity in some detail then this book is well suited to your needs.

Excellent delivery!.......2005-09-25

This book was delivered in immaculate condition and is exactly how I was hoping it would be. Thank you for your product and i hope to do business with you again!

Sincerely,

Travis

Gives an intuitive understanding of General Relativity.......2005-08-18

This book sidesteps the hard work needed to motivate and develop the Einstein field equations, and goes directly to one of the most important solutions of the equations, the Schwarzschild solution, which gives rise to the concept of a black hole. By exploring what observers in different parts of space-time would experience along their different trajectories (whether falling into a black hole or watching from a safe spot far away), Taylor and Wheeler manage to convey an intuitive understanding for such typical GR "paradoxes" such as the fact that the same "event" (the crossing over of an object through the event horizon) can be seen to take 15 minutes, or forever, depending on who's watching it.

Because of what it omits, this book is not a complete presentation of GR. It does present the most fun part of GR, however, in a way that is mathematically accessible.

Along the way, a few side questions are adddressed, like "How painful would it be to be squished/torn apart as I fall into a black hole?" A lot of time is also spent explaining how the weird trajectories of light within the event horizon will transmogrify what is seen by the observer.

This is a great book and a lot of fun. I am also left with a greater motivation to go back to a more complete presentation, to be convinced that "this is where you have to end up". Although much longer, this book is a worthy successor to the original output of this dynamic duo, "Spacetime Physics".

An Introduction to Relativistic Quantum Field Theory

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An Introduction to Relativistic Quantum Field Theory
Silvan S. Schweber
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486442284

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In a relatively simple presentation that remains close to familiar concepts, this text for upper-level undergraduates and graduate students introduces modern developments of quantum field theory. "Combines thorough knowledge with a high degree of didactic ability and a delightful style." — Mathematical Reviews. 1961 edition.

Lagrangian Interaction: Introduction To Relativistic Symmetry In Electrodynamics And Gravitation

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Emphasis here is on symmetries.
A superb book
Very good introduction to Lagrangian mechanics.
An excellent readable introduction to Lagrangians in physics

Lagrangian Interaction: Introduction To Relativistic Symmetry In Electrodynamics And Gravitation
Doughty
Manufacturer: Westview Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0201416255

Customer Reviews:

Emphasis here is on symmetries........2006-10-31

I was expecting something along the lines of an updated Lanczos (The Variational Principles of Mechanics). But the emphasis here is very much on relativistic symmetries. Actually the book reminds me somewhat of Penrose's _Road to Reality_ and -- perhaps a better comparison -- Longair's _Theoretical Concepts in Physics_, with a mix of popular and semi-popular exposition, historical background, and more detailed mathematical exposition, but with a focus on relativistic symmetry (which still allows for a pretty wide-ranging number of topics in physics).

One complaint: the paper, printing and artwork are rather poor for a $45 paperback. Oxford and Cambridge Press, for example, produce much higher quality paperbacks in this price range. I've knocked off a star for that.

A superb book.......2001-10-24

This is work is comprehensive, easy to follow, and well-formatted. It is an excellent introduction to the action principle. It also serves as a great primer for the mathematics of special relativity, 4-vectors, vector fields and tensors. It is a shame that it doesn't go very far into GR (from the least action perspective) though.

Very good introduction to Lagrangian mechanics........1998-06-19

I highly recommend this book to undergraduate and graduate students in physics and astrophysics. It's clearly written, with a very modern approach (and book design!).

An excellent readable introduction to Lagrangians in physics.......1998-05-27

This is an excellent book. It is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity

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Special Relativity for the graduate student.
Fascinating but not for the general reader

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity
Gregory L. Naber
Manufacturer: Dover Publications
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ASIN: 0486432351

Book Description

This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; the theory of spinors; and more. 1992 edition. 43 figures.

Customer Reviews:

Special Relativity for the graduate student........2007-01-18

This book is NOT for the pop science buff or the novice with little understanding of Special Relativity.

This book is designed for graduate level students in mathematics or physics who want a deeper understanding of Minkowski space. It presupposes a solid foundation in SR.

Having said this, the book is phenomenal. It brings out startling relationship between mathematics and physics explaining esoteric phenomena in SR.

For example:

1) The author shows how Lorentz transformations can be realized as fractional linear transformations of the Riemann sphere. By doing so we can use the full power of complex analysis to derive far reaching results. One property of such tranforms is that they map circles to circles thus explaining why an observer at rest who sees a circle ( say lit by lights ) will also see a circle, NOT ellipse from length contraction, when he moves relative to the circle.

2) Using a simple example ( scissors, chair and rubber band ) the author shows how a 360 degree rotation may not leave a system in the same state requiring the need of a new mathematical object ( spinor ) to describe this transformation.

3) The author clearly develops the mathematics of spinors. In fact this is the best introduction to spinors I have read. He develops the notion of spin vectors and realizes spinors as multi-linear functionals with inputs as spin vectors, their duals, their conjugate, and the conjugate duals. He then lays out the transformation properties of the spinors and shows that certain spinors have exactly the transformation properties needed to model particles with spin.

4) There is a great section on the relationship of SL (2,C) to the lorentz group. The author shows how Minkowski space can be represented by certain combinations of 2x2 complex matrices and shows how SL ( 2,C) can then operate on these. This operation is actually equivalent to a lorentz transformation thus giving a mapping between the two groups. He then shows that we can easily analyze SL (2,C) by breaking it down into irreducible representations ( which are known ) and that to each of these representations there exist a unique representation of the Lorentz group ( provided certain conditions are imposed ). If that condition is not met the representation leads to the all familiar 2-valued representation of the Lorentz group one hears so much about. Thus by studying SL ( 2,C ) which we know alot about we can represent the Lorentz group which is generally harder to study but of the most relevance in physics.

The books is filled with such insights and I would recommend it to anyone who wishes to understand particle physics or relativity.

Fascinating but not for the general reader.......2006-06-29

Starting with a quick overview of certain structures from linear algebra (bilinear forms) the book moves to discussing Minkowski spacetime. Unfortunately for many, the text is highly esoteric without even a single descriptive section that doesn't make use of some fairly advanced mathematics.

The level of mathematical maturity required is comparable to a fourth year mathematics major at any decent university. The relationship between the mathematics involved and the special theory of relativity is fully explained.

A solid introduction to special relativity for the earnest mathematician.

Introduction to the theory of relativity and the principles of modern physics (A Blaisdell book in the pure and applied sciences)

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Introduction to the theory of relativity and the principles of modern physics (A Blaisdell book in the pure and applied sciences)
Huseyin Yilmaz
Manufacturer: Blaisdell Pub. Co
ProductGroup: Book
Binding: Hardcover

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ASIN: B0006BM13M

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Introduction to Quantum Computation
Ioan Burda
Manufacturer: Universal Publishers
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ASIN: 158112466X

Book Description

Introduction to Quantum Computation is an introduction to a new rapidly developing theory of quantum computing. The book is a comprehensive introduction to the main ideas and techniques of quantum computation. It begins with the basics of classical theory of computation: NP-complete problems, Boolean circuits, Finite state machine, Turing machine and the idea of complexity of an algorithm. The general quantum formalism (pure states, qubit, superposition, evolution of quantum system, entanglement, multi-qubit system ...) and complex algorithm examples are also presented. Matlab is a well known in engineer academia as matrix computing environment, which makes it well suited for simulating quantum algorithms. The (Quantum Computer Toolbox) QCT is written entirely in the Matlab and m-files are listed in book's sections. There are certain data types that are implicitly defined by the QCT, including data types for qubit registers and transformations. The QCT contains many functions designed to mimic the actions of a quantum computer. In addition, the QCT contains several convenience functions designed to aid in the creation and modification of the data types used in algorithms. The main purposes of the QCT are for research involving Quantum Computation and as a teaching tool to aid in learning about Quantum Computing systems. The readers will learn to implement complex quantum algorithm (quantum teleportation and Deutsch, Grover, Shor algorithm) under Matlab environment (complete Matlab code examples).

Product Description

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems. Two theories covered by the book in great detail are the Maxwell-Lorentz electrodynamics and Yang-Mills-Wong theory.

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