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**Chicago Undergraduate Physics Bibliography**

So... You want to teach yourself about general relativity or particle theory, but you could never really find a suitable book to learn from. Or maybe you just hate the textbook in your intermediate physics class and want a better alternative. Well, here's a list of books I've come across in my wanderings through Crerar Library. I've tried to indicate roughly what the book covers and at what level, and I've tried to point out where certain books are dated or otherwise pathological. I also indicate when a book sucks.

I'm afraid you'll find that this list is heavily biased towards theory, and general relativy and particle theory in particular. That's partially because you can learn something about theory by reading a book and doing problems, but largely because I'm interested in mathematical physics. I'll try to get non-theory dorks to add their voices in the future. Meanwhile, future string theorists, enjoy yourselves!

Jim White has contributed a lot to this bibliography; his reviews are marked with a [J.W.]. I'm [A.T.] wherever confusion might result.

**CONTENTS**

- Mechanics
- Electrodynamics
- Quantum Mechanics
- Statistical/Thermal Physics
- Particle Physics
- Mathematical Methods
- General Relativity & Cosmology
- Mathematical Physics
- Quantum Field Theory
- String Theory

**Mechanics**

Kleppner & Kolenkow, An Introduction to Mechanics

A fairly sophisticated treatment of Newtonian physics. K&K has good, although sometimes dry, discussions of the physical principles, contains a goodly number of non-trivial examples, and has problems which require physical intuition and mathematical skill. Good for building up your technical know-how, which is why it's used in PH141. I'm not a fan of its chapters on special relativity; for all their 4-vector notation they're not very geometrical. It bugs me that the most modern elementary mechanics textbook still uses imaginary time instead of just introducing the Minkowski metric.

Feynmann, R.P., Leighton, R.B., & Sands, M.L., The Feynman Lectures on Physics, Vol. I

[J.W.] When senior faculty members at CalTech want to sit in on a freshman mechanics class, the lectures have to be pretty stellar. And they are. Leighton and Sands compiled Feynman's lectures into a phenomenally readable book that anyone serious about physics should check out at least once. In general, the lectures are pretty basic (you only need some calc), but Feynman was born somewhere near the Crab Nebula, so his insight into physics is significantly greater than that of most humans. Even now that I'm quite a bit beyond introductory mechanics, I still find myself going back to the Feynman Lectures to validate my intuition, or just to enjoy some of his remarkably insightful, lucid expostions. This is really physics bathtub reading at its best.

[A.T.] I just want to add that, in addition to treating the essential principles brilliantly, Feynman often discusses really interesting real world applications like color vision and Brownian motion.

Marion, J.B. & Thornton, S.T., Classical Dynamics of Particles and Systems

This book sucks. It offers little physical insight. Its derivations are labored rather than elegant or intuitive. Its problems are often trite, or so unclearly worded that you can't figure out what the question is. It uses cumbersome, unnecessary mathematical formalism. There is another book which uses classical mechanics to familiarize it's readers with the math needed for quantum, Goldstein's Classical Mechanics; Marion & Thornton reads like a dumbed down version of this text. It retains the formalism, but forgets the reason for using it. And it's not even heavy enough to kill roaches with! Sadly, it seems to be the only book written at its level, so almost everyone uses it in their second mechanics course.

Calkin, M.G., Lagrangian and Hamiltonian Mechanics

An advanced undergraduate level treatment of analytical mechanics. Calkin is a good book: It has interesting problems, more concerned with extensions of the theory than applications of it, and it treats a number of topics which are rarely found at the undergraduate level: Noether's theorem, for instance. Unfortunately, it's awkwardly typeset, and sometimes uses cumbersome notations.

Landau, L.D., Lifschitz, E.M., Course of Theoretical Physics, V. I: Mechanics

Lev Landau was one of the giants of 20th century physics. And his 10 volume Course of Theoretical Physics contains about half of my favorite physics books. Landau's books are all gems: elegant, sophisticated treatments of their subjects, filled with unique theoretical insights and clever derivations. However, the master is hard to imitate; you may find that his books don't prepare you to solve problems. (Landau's books contain few problems, and these have the answers right below them.) Look on the bright side though; at least now you know that there exists a singularly beautiful way of looking at physics.

Mechanics is, of course, no exception to all of this. Of particular note are its derivation of the free particle Lagrangian from physical principles, and its treatment of the Hamilton-Jacobi equation.

[J.W.] Landau writes the kind of books that you read the first time and think, "What does this have to do with anything?" Then, once you really know the subject, you read it again and think, "Wow, that's really brilliant!!!" Landau's book on mechanics, like many of his books, is not a good first book. However, once you're pretty comfortable with mechanics, it's deeply insightful and a real pleasure to read.

Goldstein, H., Classical Mechanics

Was and probably still is, the canonical graduate-level mechanics textbook. Goldstein uses classical mechanics to introduce his readers to the mathematical apparatus of quantum mechanics, so you'll find lots of linear algebra here. Goldstein is worth studying for this reason alone. It also contains nice expositions of special relativity and classical field theory. Nice problems, too.

[J.W.] What A.J. said. If you want to learn mechanics, and you have math, read Goldstein, then read Landau. There's really no good reason to look at anything else.

Arnol'd, V. I., Mathematical Methods of Classical Mechanics

This is the book used in the U of C's graduate mechanics class, which acquired a bit of a reputation for kicking people's asses. It should really be called Geometrical Methods of Classical Mechanics. Arnold uses the methods of modern differential geometry--manifolds, tangent bundles, variational calculus, differential forms, symplectic spaces--to study classial mechanics. (I suspect that grad classes use Arnol'd to introduce some of the math needed to study gauge theories, just as they use Goldstein to introduce the math needed to study quantum mechanics.) I really like the book; I think its rigorous use of math clarifies a lot of subtlties in classical physics. I also think it's amusing that it contains over 200 pages of appendices.

**Electrodynamics**

Purcells, E.M., Electricity & Magnetism

Purcells' book is a really superb introduction to electromagnetism. It's largely devoted to deducing Maxwell's equations in a quasi-historical fashion: Purcells thesis is (roughly) that Gauss's Law, Lorentz invariance, and some other assuptions give you electromagnetism. Also, many of its problems fall into the class of "You should work this out for yourself at least once in your life."

[J.W.] Rumor has it around HEP that Purcells is the book that convinced Dr. Abella to go into physics. It came from Dr. Frisch so it's probably true. My one (minor) complaint is that, in the last few chapteres, Purcells occasionally tries to pull the wool over your eyes to protect you from what really happens. Otherwise, it's a fabulous book and certainly the first book you should read to learn E & M.

Griffiths, D.J., Introduction to Electrodynamics

Griffiths does a pretty nice job of filling in the gap between Purcells and Jackson. It's one of the most loved textbooks in physics--partly because most physicists just plain like electrodynamics, and partly because Griffiths is one kickass pedagogue. (His physics colloqium in '99 was better attended than the one given by the previous year's Nobel Laureate.) His problems are good and instructive; his exposition is clear and gentle. You couldn't ask for a better intermediate electrodynamics textbook.

Wangsness, R.K., Electromagnetic Fields

[J.W.] Mathematically very precise, Wangsness frequently doesn't read like a physics book. It tends to get lost in mathematical formalism which it forgets to motivate, so reading it is kind of frusterating unless you already know the subject and just want a reference, for which it's pretty good. If you're forced to use it for a class, use it for the problems, but get the physics from Griffiths. Otherwise, if you have the math, just skip it and go right to Jackson. (And if you don't have the math, learn it, and skip to Jackson anyways.)

[A.T.] Jim's review is right on, but I would like to add one thing: I think Wangsness declines in quality as it moves along. Its chapters on static fields and dielectrics are really pretty good, but its treatment of radiation is badly done: somehow both complicated and superficial. I just don't like Wangsness; there are so many good electrodynamics textbooks that I can't see why this one is used in 225 & 227.

Landau, L.D. & Lifschitz, E.M., A Course of Theoretical Physics, Vol. II: The Classical Theory of Fields

Many people think this is the most beautiful of all the Landau and Lifshitz books. I don't entirely agree, but I still place CTF among the best 10 physics books ever written. Landau's discussion of electromagnetic radiation is about the best that there is. And as always, there's important physics in Landau that you won't find elsewhere. Read it, if you have time; it will improve your grasp of physics. There's not much else to be said.

Jackson, J.D., Classical Electrodynamics

For mature audiences only. The most canonical of canonical textbooks, Jackson covers just about everything you ever wanted to know about electrodynamics. This is the one physics book that every future physicist MUST read; it is used in nearly every graduate electrodynamics class in the nation. Jackson's physical reasoning is nearly always clear, if terse. His mathematical derivations are masterful. And his problems are well...legendary. Class after class of terrorized graduate students have spent uncounted late nights solving Jackson's numerous difficult problems. I used this book as my primary text in PH225 and PH227, and found it exceedingly useful. I think that if you want to learn electrodynamics, you will not find a better book.

Smythe, W.R., Static and Dynamic Electricity

I have not read this book myself, but I have been told that its problems make Jackson's look easy.

**Quantum Mechanics**

Griffiths, D.J., Introduction to Quantum Mechanics

Cohen-Tannoudji, C., Dui, B., & Laloe, F., Quantum Mechanics

[J.W.] This book really has it all. It comes in two huge volumes, sold separately at about $90 each, so for the price it should. It's a very complete, generally well-thought out portrait of quantum in all its glory. The downside is that, if you're learning quantum for the first time, there's a lot of stuff to slog through that you may not care about, and it can be hard to decide what to read and what not to read. But if you already know quantum, it makes a fantastic reference as it's clear and hyper-complete. C-T. is sometimess criticized for the complex chapter/supplement/exercise organization, but really, if you can't figure out how the chapters work, what are you doing reading about quantum mechanics?

Shankar, R., Principles of Quantum Mechanics

Shankar is a good modern introduction to quantum mechanics. It begins with a very long chapter (~80 pages) on the necessary mathematics, i.e. linear algebra & linear operators. Then it lays down the postulates of quantum physics, and goes on to a talkly, reasonably thorough study of the basic applications of quantum mechanics. It's not complete, but it doesn't pretend to be. I have two complaints: The problems are often "canned"--that is, they are easily solvable, and not so closely related to the real world. Second, the quality of the problems--their individual completeness and relevance to the text--takes a downhill turn around chapter 12.

[J.W.] More chatty than Cohen-Tannoudji, but less complete (and cheaper), Shankar is a good book from which to initially learn quantum. Once you already know the subject, you'll probably find yourself frusterated or annoyed by its sometimes superficial treatments and its general lack of sophistication, but once you've reached this point, the book isn't really meant for you anyways. Again, a good introduction.

Townsend, J.S., A Modern Approach to Quantum Mechanics

I can't point to any particular reasons that I like this book, but I do indeed like it. It's a well thought-out coherent study of the structure and essential techniques of quantum mechanics...very nice for a second reading on quantum theory. It's reads like a kind of undergraduate Sakurai, but it's got strengths that Sakurai doesn't. (For one thing, Townsend did not die midway through writing his book.) It's a little less cavalier in its derivations, and a little more careful in its expositions. I guess that's because it was intended as an undergraduate text.

Edmonds, A.R., Angular Momentum in Quantum Mechanics

My little reference on the quantum theory of angular momentum. Edmonds has efficient derivations of all of the essential theory: irreducible representations of the rotation group, spherical harmonics, Clebsh-Gordon coefficients, Wigner-Eckhardt theorem,etc,... Next to no applications and no problems, but it's come in very handy from time to time. There's usually a copy at Powell's for $6.

Dirac, P.A.M., The Principles of Quantum Mechanics

The classic exposition of quantum mechanics, written by the first person to really understand the theory, Dirac's book is usually put on the same shelf as Newton's Principia. It is still worth reading today, because it's filled with amazing insights into the structure of quantum theory. It's a distinct pleasure, to see that Dirac pays attention to all of the physical subtleties which are glossed over in more recent textbooks.

I sometimes tell people that a theoretical physicist's reputation depends on how long it takes mathematicians to turn his half-assed ideas into rigorous mathematics. It took more than a decade for mathematicians to make sense of the delta "function," and much longer than that for them to understand his bra-ket formalism. In fact, it was never really understood in one sense: It's still very easy to get non-sensical results from the formalism by pushing it in the wrong direction.

Feynman, R.P. & Hibbs, A., Quantum Mechanics and Path Integrals

Feynman must have been a greater theorist than Dirac, because no mathematician yet has really made sense of his path integral formalism. (See the review of Dirac's book above.) Nonetheless, Feynman's book is a worthwhile read. It's still the nicest exposition of the subject I've seen, packed with typical Feynman insights. Besides, it's worth reading just to see what Feynman had in mind. (His notion of defining path integrals as suitably regularized limits of normal integrals is essentially the only way of dealing with the damned things in anything resembly a rigorous manner.)

Schiff, L., Quantum Mechanics

I've been told that (a) Schiff's book is really just a transcription of Oppenheimer's Berkeley lectures on quantum theory, updated at suitable points, and (b) that it's rife with errors and typos. I don't know about the truth of either of these, because I've never used Schiff as anything but a reference. It's a pretty complete coverage, and despite an occaionally annoying typeset, it's good for looking things up.

Landau, L.D., A Course of Theoretical Physics, Vol. III: Quantum Mechanics

Typical Landau: efficient, elegant exposition of the subject, packed with brilliant insights and covering topics you absolutely will not find elsewhere. In particular, Landau's discussion of the measurement processs in terms of wave functions may be the single most amazing piece of physics I've ever seen. The problems are also particularly good in this one, and the special functions appendix is extremely useful.

Sakurai, J.J, Modern Quantum Mechanics

A popular graduate text, Sakurai's book really does live up to its title: It uses symmetry as an organizing principle, and this is the hallmark of modern physics. The text is, for the most part, well-written, and it contains a host of good problems. Mathematics is sometimes given short-shrift here--hard to avoid in a text for a general physics audience--but the physical reasoning usually makes up for it. Unfortunately, Sakurai died before completing his book, and the later chapters are not as good as the early ones.

Merzbacher, E., Quantum Mechanics

Another popular graduate text, Merzbacher is not as modern as Sakurai in its emphasis, but it covers a much broader range of topics. Sakurai's book is better for the basic principles, but Merzbacher's is better for things like scattering theory and approximation techniques and all of their various applications.

**Thermal/Statistical Physics**

Hill, T., An Introduction to Statistical Thermodynamics

You won't get a better deal for your dollar if you're looking for an introduction to basic statisitical physics. Hill is a Dover, so it costs about $10. Of course, being a Dover, it's rather old, so its notation and selection of applications may seem a little bit dated. But it's first several chapters are a very solid exposition of the basic concepts: ensembles, fluctuations, and partition functions. After that, it's more geared towards chemical physics; there's a lot of cool stuff on non-ideal gases, liquid perturbation theory, and the like. If you don't like Reif for 197, you should consider using this instead.

Hill, T., Statistical Mechanics: Principles & Selected Applications

More advanced than Hill's Introduction to Statistical Thermodynamics, but covering pretty much the same material. Hada good explanation of the cluster expansion, if I remember correctly.

Reif, F., Fundamentals of Statistical & Thermal Physics

A huge, rambling book which is used in 197, Reif has something to say about just about everything. Unfortunately, he usually has more to say than you want to listen to; crucial points are often obscured by protracted discussion and excessive mathematical manipulation. You sort of need to read between the lines to extract the important stuff, but that shouldn't be a problem if you have a good prof. And to Reif's credit, it has a lot of neat problems.

Goodstein, D., States of Matter

Another very place to look if you're annoyed with Reif, or if you want to learn a little about more modern statistical physic (such as superconductivity). Goodstein opens with an excellent discussion of statistical thermodynamics/mechanics (which he says was inspired by Landau), and then surveys a bunch of cool stuff from solid state and condensed matter physics. Goodstein is a wonderful expositor, and not afraid to tell a joke or two in the course of teaching. I envy the CalTech students who took the class this book is based on. A Dover paperback, too, which is surprising, because it's actually a relatively recent text (i.e. newer than Reif).

Tolman, R.C., The Principles of Statistical Mechanics

Landau, L.D. & Lifschitz, E.M., Statistical Physics, Vol. I

Landau, L.D., Statistical Physics, Vol. II

**Particles Physics**

Perkins, D.H., Introduction to High Energy Physics

Perkins is a (relatively) unmathematical introduction to particle physics. If you think of it as a book for experimental physicists who need to know a few things about the math, or as a book for theorists who need to know a few things about detectors and scattering experiments, you won't be far from the mark. Perkins contains a lot of information, especially in the form of plots and figures. I didn't find it all that enlightening. It is the most recent particle physics book I could name, so look here if you get tired of hearing "the top quark has not yet been discovered."

Gottfried, K. & Weisskopf, V., Fundamental Concepts of Particle Physics

Not so much a textbook as a set of spruced up lecture notes, Gottfried & Weisskopf is useful for learning a few things about the "concepts of particle physics" and not so useful for learning how to calculate things.

Halzen, F. & Martin, A.D., Quarks & Leptons: A Modern Introduction to Particle Physics

The best book I know about...well, about quarks and leptons and their interactions. Halzen & Martin is clear and coherent and strikes a good balance between high-falutin theory and honest to God experimental phenomena. Most importantly, it does a good job and getting the basic concepts of particle theory across, and teaching you how to calculate Feynman diagrams. Don't look here for field theory, though; this is a book about particles.

**Mathematical Methods**

These are books which you might consult after you've reduced your physics problem to a set of equations to be solved. Some of them also purport to teach the reader "the mathematical methods of physics." I think this is bullshit. If you want to use math, learn to use it the way mathematicians do. For hints on how to do this, go look at Chris Jeris's Chicago Undergraduate Math Bibliography.

Gradshteyn, I.S., Ryzhik, J.M., Ryzhik, I.M., & Jeffrey, A., Table of Integrals, Series, and Products

If you want it, it's in here in one form or another. This is the book to consult when you've got an integral you can't solve on your own. The tome's authors have tabulated something like 20,000 integrals. (There's an amusing story here, possibly apocryphal: The authors of the original edition spent about a year locked in a cabin in Siberia just doing integrals. Supposedly, they measured an integral's difficulty by counting how many vodkas they needed to drink before finding a solution.) Unfortunately, the solution to those nasty integrals often involve the so called "special functions."

Arfken, G.B. & Weber, H., Mathematical Methods for Physicists

This is the standard mathematical methods textbook. It's really not much more than a big collection of formulae and pseudo-derivations. It'll be useful if you can't remember what the 3,1 spherical harmonic looks like, but it's not even all that useful as a reference book, because many of the formula you might need are hidden in the exercises rather than in the main text. I suppose it's probably quite a learning experience to go through and work all the problems, but this is more likely to leave you with a head full of formulae than a good understanding of how to apply math to physics problems. A better book for that is...

Mathews, J. & Walker, R.L., Mathematical Methods of Physics

Based on a course Feynman gave at Caltech, this book is not a reference book, not comprehensive, but it does a nice job at teaching you how to apply math to solving physics problems. Contains a lot of useful tricks and techniques. Probably contains all the math you'll ever need for an undergraduate course.

**General Relativity & Cosmology**

Schutz, B., A First Course in Generaly Relativity

Schutz's book is a really nice introduction to GR, suitable for undergraduates who've had a bit of linear algebra and are willing to spend some time thinking about the math he develops. It's a good book for audodidacts, because the development of the theory is pedagogical and the problems are designed to get you used to the basic techniques. (Come to think of it, Schutz's book is not a bad place to learn about tensor calculus, which is one of the handiest tools in the physics toolkit.) Concludes with a little section on cosmology.

Dirac, P.A.M., General Relativity

You might have heard that Paul Dirac was a man of few words. Read this book to find out how terse he could be. It develops the essentials of Lorentzian geometry and of general relativity, up through black holes, gravitational radiation, and the Lagrangian formulation, in a blinding 69 pages! I think this book grew out of some undergrad lectures Dirac delivered on GR; they are more designed to show what the hell theory is all about than to teach you how to do calculations. I actually didn't like them all that much; they were a little too dry for my taste. It's amusing though, to put Dirac's book next to the book of Misner, Thorne, and Wheeler. D'Inverno, R., Introducing Einstein's Relativity

I think that D'Inverno is the best of the undergraduate texts on GR (an admittedly small group). It's a tad less elementary than Schutz, and it has a lot more detail and excursions into interesting topics. I seem to remember that it's development of necessary mathematics struck me as somehow lacking, but unfortunately I don't remember what exactly annoyed me. But for physics, I don't think you can beat it. Just be careful: you might find that there's a bit too much here.

Landau, L.D. & Liftschitz, E.M., The Classical Theory of Fields

The second half of the Classical Theory of Fields is a quick overview of GR and cosmology. The exposition is efficient and clear as always, but the chapters don't cover very much and are slightly dated. Still worth reading, though.

Misner, C., Thorne, K., & Wheeler, J.A., Gravitation

Gravitation has a lot of nicknames: MTW, the Phonebook, the Bible, the Big Black Book, etc,... It's over a thousand pages in length, and probably weighs about 10 pounds. It makes a very effective doorstop, but it would be a shame to use it as one. MTW was written in the late 60's/early 70's by three of the best gravitational physicists around--Kip Thorne, Charles Misner, and John Wheeler--and it's a truly great book. I'm not sure I'd recommend it for first time buyers, but after you know a little about the theory, it's about the most detailed, lucid, poetic, humorous, and comprehensive exposition of gravity that you could ask for. Poetic? Humorous? Yep. MTW is laden with stories and quotations. Detailed? Lucid? Oh yes. The theory of general relativity is all laid out in loving detail. You will not find a better explanation of the physics of gravitation anywhere. Comprehensive? Well, sorta. MTW is a little out of date. MTW is good for the basics, but there's actually been quite a bit of work done in GR since it's publication in 1973. See Wald for details.

Wald, R., General Relativity

My favorite book on relativity. Wald's book is elegant, sophisticated, and highly geometric. That's geometric in the sense of modern differential geometry, not in the sense of lots of pictures, however. (If you want pictures, read MTW.) After a concise introduction to the theory of metric connections & curvature on Lorentzian manifolds, Wald develops the theory very quickly. Fortunately, his exposition is very clear and supplemented by good problems. After he's introduced Einstein's equation, he spends some time on the Schwarzchild and Friedman metrics, and then moves on into a collection of interesting advanced topics such as causal structure and quantum field theory in strong gravitational fields.

Stewart, J., Advanced General Relativity

Stewart's book is often for sale at Powell's, which is why I've included it in this list. It's coverage of differential geometry is very modern, and useful if you want some of the flavor of modern geometry. But it's topics are all covered in Wald's book and more clearly to boot.

Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity

Weinberg's book is an interesting piece of work. Like a lot of Weinberg's work, it is directed at his colleagues, future and present, and serves to proselytize a viewpoint of his. He wrote this book because he thought that general relativity was too heavily tied to differential geometry, and wanted to demonstrate that it could be done without reference to geometry. (I've read that what he was really trying to do was make GR more amenable to the language of particle physics.) Weinberg takes the Equivalence Principle as his foundation, and proceeds towards Einstein's equation in a rather careful way, making frequent contact with the experimental evidence. It's an educational read, but not really all that great as a textbook, if you ask me.

Peebles, J., Principles of Physical Cosmology

One of possibly several books by Peebles, a respected cosmologist. Often available at Powell's for cheap. Mostly about galaxies and clusters, and structure formation, and other topics from the matter-dominated era. I've only read bits and pieces of it, but I can tell you that it's interesting and fairly comprehensive. Just make sure you check your copy before you buy; my friend Will got a copy with some spectacular misprints from Powell's.

Kolb, E. & Turner, M., The Early Universe

Pretty much the definitive reference about its subject, The Early Universe is mostly about the first minute or so after the big bang. It's a real good place to learn about the ties between cosmology and particle physics.

**Mathematical Physics**

I've included in this section any book which is primarily about the math we use to do physics or about the proper mathematical foundations of some branch of physics (e.g. quantum field theory).

von Neumann, J., Mathematical Foundations of Quantum Mechanics

One of the great classics. von Neumann put quantum mechanics on mathematically rigorous footing, and introduced a lot of important ideas along the way: density matrices, Hilbert spaces & linear operators thereon, operator algebras. Read this for its historical value.

Baez, J., Gauge Fields, Knots, and Gravity

This is a really cool book. John Baez has a rare talent for making physicists understand how high powered mathematics works. GFK&G is an introduction to the use of fiber bundles in gauge theory. He develops the mathematics first using electromagnetism (i.e. U(1)) as his example, then goes on to introduce his reader to Abhay Ashtekar's reformulation of general relativity. Ashtekar's formulation of GR makes it look more like a standard gauge theory; it's the foundation of the canonical quantum gravity program. Baez has also filled his book with good problems, which range in difficulty from the trivial "show this" to the last problem in his book, which is far and away the hardest problem I've ever seen in a textbook.

Geroch, R., Mathematical Physics

This is one of my favorite books. Geroch used to be a professor in the math department before he joined the physics department, and his book reflects that. He uses category theory to give his reader a grand overview of topology, algebra, and analysis as applied to physics. It's a top down approach, beginning with categories, which are about the most general structures in mathematics, and specializing to everything else. I think this book should be mandatory reading for physics students; it'll teach them a lot about the proper use of mathematics, and the benefits of using math correctly.

Jauch, J.M., Foundations of Quantum Mechanics

Haag, R., Local Quantum Physics: Fields, Particles, Algebras

Haag was one of the founders of algebraic quantum field theory, which was an attempt to put quantum field theory on some sort of rigorous foundation. (AQFT was a partial success; it managed to come up with some criteria a theory must satisfy.) Local Quantum Physics is Haag's thoughts on what quantum theory is and what it should be. It's a difficult read; you'll need a lot of mathematical training just to understand it. But it's rewarding, because Haag's discussion of the fundamental principles and concepts of field theory is about the clearest I've ever seen.

Glimm, J. & Jaffe, A., Quantum Physics: A Functional Integral Point of View

Constructive QFT followed algebraic QFT; it was an attempt to produce mathematically well-defined interacting QFT's. Like AQFT, CQFT was a partial success; they managed to prove some things about QFT's in 2 and 3 spacetime dimensions, but didn't come anywhere near proving interesting results about the theories we use to describe the real world. This book is a summary of their results. It's interesting if you're interested in this sort of thing.

**Quantum Field Theory**

Sakurai, J.J., Advanced Quantum Mechanics

If you're curious about quantum electrodynamics and you've had a little bit of quantum mechanics, then this is the book for you. It's not very modern--still uses imaginary time, in fact--but it's well written, and each chapter concludes with a couple of instructive problems. Sakurai will teach you all of the basics--classical field theory, S-matrices & Feynman diagrams, radiative corrections, and elementary renormalization-- and will show you few classic applications, like Compton scattering and the anomalous muon magnetic moment.

Ryder, L.H., Quantum Field Theory

I've included a review of Ryder here because there are often copies of it for sale at Powell's. Here's the deal: Ryder is a reasonably modern treatment of field theory, mostly directed at learning path integrals to study the standard model. Its rather glib and it has no problems, so it won't teach you much, but it doesn't hurt to spend $13 and a few evenings with it. You will learn a few things. But if you're really serious about field theory, find a copy of Peskin & Schroeder.

Peskin, M.E. & Schroeder,D.V., An Introduction to Quantum Field Theory

I went out and slapped down $60 for this book the same day Jeff Harvey recommended it to me. I've never regretted the purchase. Peskin & Schroeder is a really good first look at quantum field theory. Its discussion of the physics is very intuitive, and, rather than misuse high-powered math, it does what it does quite nicely with just tensor analysis and complex analysis. The book comes in 3 majors chunks: Quantum Electrodynamics, which is where you'll earn about S-matrices and Feynmann diagrams. Renormalization, which is where you'll learn about the path integral methods and the renormalization group. And Non-Abelian Gauge Theories, which is where you'll learn about asymptotic freedom and spontaneously broken symmetry. My only criticism is that Peskin & Schroeder mostly emphasize perturbative techniques. But if you want to sit down, shut up, and calculate, this is the book for you.

Kaku, M., Quantum Field Theory: A Modern Introduction

There's something just not quite right about Kaku's book. It reminds me of a pretentious but poorly educated TA; it throws a lot of fancy words around, but doesn't convey much in the way of real understanding. The book consists of a rather poor exposition of the fundamentals, followed by a series of sound bites on more advanced topics. It also doesn't help that Kaku is rather sloppy with his mathematics, or that his problems are largely uninteresting. To the book's credit, it has a reasonably good discussion of renormalization, and it has entertaining quotes at the beginning of each chapter.

Weinberg, S., The Quantum Theory of Fields, Vol. I: Foundations

This is likely to be one of the most influential physics books of the next century. However, it is not an introductory textbook; you need to be pretty damned bright to learn much about calculating cross sections from this book. Instead, it is, like Jackson and Goldstein, the definitive exposition of the subject. Weinberg, one of the co-inventors of the electroweak theory, has set out to explain why quantum field theory is quantum field theory. His basic thesis is that the requirements of Poincare invariance and locality (as expressed in the cluster decomposition principle) conspire to make any theory of fundamental physics look like a theory of quantum fields when viewed at low enough energies that that the fundamental constituents of matter behave like particles. Weinberg is sometimes dry and difficult, but his argument is so interesting in its own right that he can be forgiven. His book requires a lot of the reader; you will need to think very carefully to make sure you agree with the steps in his arguments, and you may need to teach yourself a good deal of unfamiliar math. I would recommend reading this book after you've studied Peskin & Schroeder to become familiar with the basic computational apparata. I would also like to note that Weinberg's ideas appear to owe a great deal to the work of Rudolf Haag and the algebraic quantum field theorists of the 1960's.

Weinberg, S., The Quantum Theory of Fields, Vol. II: Modern Applications

The title pretty much says it all. This is a very thorough study of gauge invariance, modern quantization and renormalization methods, and spontaneous symmetry breaking. It is by far the most modern exposition of these subjects. It reads at about the same level as Vol. I, but I believe its contents are a little less controversial. (Several U of C theorists have commented to me that they didn't completely buy Weinberg's argument in Foundations, but are quite happy with Modern Applications.)

Wald, R., Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics

**String Theory**

Caveat emptor! I'm really not qualified to judge these books. However, I've looked at them, and I can tell you a few things about them. If nothing else, they should be included for the sake of completeness; this is an undergraduate bibliography after all. :)

Green, M., Schwarz, J., & Witten, E., Superstring Theory, Vol. I & II

The old standard in string theory; Green and Schwarz were guys who got everyone interested in strings by showing that it automatically contained a graviton, and Witten is Witten, the foremost theoretical physicist of our times. GSW is slightly old now; it was written in 88 and doesn't contains a lot of the recent developments like duality and M-theory. It's still quite interesting to read; you can learn a lot about field theory by studying this book. And if you want to do string theory, you'll probably have to read it anyways.

Polchinksi, J., String Theory, vol. I & II

A much newer book on strings, published in 98. Much more modern in its emphasis and choice of topics, and a good bit more pedagogical. Read here if you want to learn about things like T-duality or D-branes.

## Comments

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TopNewestThis is a very very useful piece of information . But for right now I need to study some important concepts like calculus , number theory etc.Can you tell me about some websites from where I can study online about concepts of physics and maths. – Raven Herd · 3 years, 2 months ago

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– Ananth Jayadev · 1 year, 6 months ago

You can get the book "What is Mathematics?" by Richard Courant and Herbert Hobbins, revised by Ian Stewart.Log in to reply

note. – حكيم الفيلسوف الضائع · 3 years, 2 months ago

There are tons of websites out there but there's nothing better than getting a textbook. For maths topics like calc, nt... check thisLog in to reply