I'm having a hard time trying to get my head around the fundamentals of gauge theory. I've taken classes in QFT and Particle Symmetries recently, both of which touch on the topic, but neither explained it in detail. Browsing the Wikipedia entry on gauge theory gives me the same heuristic arguments I've read hundreds of times, together with some mathematical formalism that's totally impenetrable.  Does anyone know of an introductory book that will explain gauge symmetries, the gauge group and their applications to a grad school student? Ideally I'd like a book which starts slowly but gets far, and isn't too basic. However I'm not looking for a text where you need to have done a couple of courses in differential geometry (fibre bundles etc) to get started!
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I am looking for a preferably introductory text on Yang-Mills theory with mathematical basis and language. (Differential forms) I have a background in QCD and QED, however, I want to go more in details in geometrical interpretations of Yang-Mills theory. I am sorry if this question has asked before. Thanks in advance.
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I am looking for an introductory textbook on QFT in curved space-time via the path integral method. I want to understand the following:   How to build a generic perturbative QFT in curved space-time Are there some specific difficulties with normalization How to derive observables / particle states in curved space-time The Unruh effect The Hawking radiation   I would appreciate if the author would use path integrals instead of the canonical formalism when possible. The reason for this is purely aesthetic.
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I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth?
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I know classical physics, quantum mechanics, special relativity, and basic nuclear physics. I would like to get into some particle physics.   Where can I find a good introduction? It might be useful to segment books by whether they require quantum field theory or not.
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I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.  Are there any good books or other reference material which can help in learning about quantum field theory? What areas of mathematics should I be familiar with before reading about Quantum field theory?
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I've been watching  and in one lecture, he discusses a very simple gauge theory.  We have a complex scalar field $\phi(x)$ with Lagrangian  $$\mathscr{L} = \partial_\mu \phi^* \partial^\mu \phi - V(\phi^* \phi)$$  and we want to do the gauge transformation $\phi(x) \to e^{i\theta(x)} \phi(x)$.  But the derivative term in the Lagrangian is not invariant if $\theta$ varies from place to place, so we add a new vector field $A_\mu$, and define it to transform like $$A_\mu \to A_\mu + \partial_\mu \theta$$ under the gauge transformation.  Then we change the Lagrangian to use covariant derivatives $D_\mu = \partial_\mu + iA_\mu$ instead of ordinary ones; now when the gauge transform is done all the derivatives of $\theta$ cancel out, and the result is invariant.  My question is: was there any freedom in choosing to add a vector field, with that specific gauge transformation law?  Are there any other ways we could get gauge invariance here—by using a different transformation law, or with a different type of field (say, a scalar, tensor, or spinor) with some other transformation law?  More generally, how can we tell what type of field is needed and what its gauge transformation law should be, to get some particular Lagrangian to be invariant under some particular gauge transformation?
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What would be your recommendation for the text which could be useful for someone starting with lattice theory? Suggestion for both books and online materials/lecture notes are welcome.    This was asked as a part of  and I did not like that it was combination of two different questions. (One of them on geometric modular lattices and the other one about text recommendation.)  I don't expect the user to post a follow-up question, since he was not seen at MSE for some time. I think that this could be a useful for some users here, so I've decided to post it myself.
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Of course, assuming your grandmother is not a theoretical physicist.  I'd like to hear the basics concepts that make LQG tick and the way it relates to the GR. I heard about spin-networks where one assigns Lie groups representations to the edges and intertwining operators to the nodes of the graph but at the moment I have no idea why this concept should be useful (except for a possible similarity with gauge theories and Wilson loops; but I guess this is purely accidental). I also heard that this spin-graph can evolve by means of a spin-foam which, I guess, should be a generalization of a graph to the simplicial complexes but that's where my knowledge ends.  I have also read the  but I don't find it very enlightening. It gives some motivation for quantizing gravity and lists some problems of LQG but (unless I am blind) it never says what LQG actually is.  So, my questions:        Try to give a simple description of fundamentals of Loop Quantum Gravity.   Give some basic results of the theory. Not necessary physical, I just want to know what are implications of the fundamentals I ask for in 1.   Why is this theory interesting physically? In particular, what does it tell us about General Relativity (both about the way it is quantized and the way it is recovered from LQG).
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I was asked to read about Graph Theory. First got the book "Graph Theory with Applications" by Bondy and Murty. As a Computer Science student its becoming difficult to read and understand. Then I started reading "Graph Theory-Modeling, Applications and Algorithms" by Agnarsson and Greenlaw. They presented the same topics little bit easier but from a different point of view. I found the definitions are bit different. But they essentially mean the same.  I am looking for some books on Graph Theory for a Computer Science student from a beginner point of view. I am looking for books like "Graph Theory-Modeling, Applications and Algorithms".
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I'm interested in reading Dr. Peter Woit's article, Quantum field theory and representation theory: a sketch .  What math and physics background would be needed?  (A list of topics from the two fields would be more than sufficient.)  With great appreciation and regards.
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I have a hazy notion of some stuff in differential geometry and a better, but still not quite rigorous understanding of basics of differential topology.  I have decided to fix this lacuna once for all. Unfortunately I cannot attend a course right now. I must teach myself all the stuff by reading books.  Towards this purpose I want to know what are the most important basic theorems in differential geometry and differential topology. For a start, for differential topology, I think I must read Stokes' theorem and de Rham theorem with complete proofs.   Differential geometry is a bit more difficult. What is a connection? Which notion should I use? I want to know about parallel transport and holonomy. What are the most important and basic theorems here? Are there concise books which can teach me the stuff faster than the voluminous Spivak books?  Also finally I want to read into some algebraic geometry and Hodge/Kähler stuff.  Suggestions about important theorems and concepts to learn, and book references, will be most helpful.
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I'm not a physicist but I'm interested in , and I do not know how to start learning about it. What would be a good book to read to start learning about this topic?
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I was hoping you guys could recommend reading material on quantum information. I have a good background in quantum mechanics, including in foundational issues, as covered in Ballentine's Quantum Mechanics.  I am interested in the intersection of quantum information and quantum foundations, such as in the works of C. Fuchs and in the research of the Perimeter Institute. While I prefer a more rigorous text, I'm trying to be as open as possible and would enjoy any suggestions or recommended reads.  Currently, I am reading the book by Busch, Lahti and Grebowski, notes on ArXiv by Keyl and also the notes by Preskill.
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I am a student of 11th grade and i have completed the syallabus of both 11th and 12th grade maths with complete understanding and it was possible coz of the love for this subject that i have. I don't want to sound "larger than life" here, but my curiousity has now increased to learn maths at a deeper level. As of now i am reading "Linear algebra done right" by Axler. Thats an amazing piece of work and now i truly understand what "matrix" is all about. I also want to extend my knowledge on the following topics :  1) Algebra (groups,subgroups,homomorphisms etc)   2) Analysis   3) Geometry/Topology  Why i am here is because i wanted you guys to recommend a book on each of the above topic that would be appropriate for a beginner like me (I must mention here I have been working on Apostol's volume 1 calculus, thats a great text, but for a beginner, its best if the concept is explained in a broad manner and in as simple and easy words as possible) . I just want a book which explains the concept broadly rather than coming to the conclusion directly (which is not a great sight for a beginner like me) .   Having said that, no book is complete i understand. Thats why i am asking your recommendation as you guys are aware which text would be the best to start with for a beginner. I have searched on the net about this, but there are dozens of works available, and out of them all , i want the one which is the best (approximation) for a beginner .   Please don't misunderstand me in any way. I am just confused which text to go for, and i understand the books which u may suggest may be for undergraduate level course as these topics are for undergraduate level courses, thats not a problem at all . I need a easy to learn (i mean easy in terms of "broad" explanation) book. I hope you guys don't mind me questioning such a question on this forum . Thanks for all the help you guys have been providing me on this forum . Maths Maths Maths... the world is beautiful coz of u! :))
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I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate calculations.  Regarding this I have a few questions:   Why is it called a symmetry if it is not a symmetry? what about Noether theorem in this case? and the gauge groups U(1)...etc? Does that mean, in principle, that one can gauge any theory (just by introducing the proper fake degrees of freedom)? Are there analogs or other examples to this idea, of introducing fake degrees of freedom to facilitate the calculations or to build interactions, in classical physics? Is it like introducing the fictitious force if one insists on using Newton's 2nd law in a noninertial frame of reference?
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I am almost finishing Gilbert Strang's book "An introduction to linear algebra" (plus video lectures at MIT OCW). First and foremost, I would like to suggest this course for everyone. It has been incredibly illuminating.   I would like to continue studying linear algebra, with particular focus on different properties of matrices and the transition to more general linear spaces (I am a physicist so Hilbert spaces and etc. are of particular interest).   Does anyone have a a good recommendation of books/resources/etc.?
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I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on  to read it comfortably. Landau &amp; Lifshitz's book is not helping as its content and topics are very much different.