I liked the Bailin & Love books on Gauge Field Theory and SUSY, also Peshkin and Schroeder on QFT.
If you want to go back QED done through propagators (old style), I recommend:
Quantum Electrodynamics, W Greiner and J Reinhardt, 3rd ed., Springer. Another pedagogical text, this book presents, detail by detail, QED the old fashioned way, the way people, including Feynman, first developed QED. I believe this is an essential read if you want to understand QFT, including some of the early issues with divergences.
Advanced Quantum Mechamics by Sakurai, Addison-Wesley Publishing Company, 1967 is also good for QED.
For QFT, I storngly recommend Quantum Field Theory, 2nd ed., L. H. Ryder—This is a very well written introductory text on QFT up through introductory supersymmetry (SUSY). Ryder surveys relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then the gauge fields. In chapter 3, Ryder carefully explains the principle of minimal coupling by requiring local invariance of, firstly, the Lagrangian for the complex scalar field before moving on to treat Yang-Mills fields. Also in chapter 3, Ryder points out the parallels originating from parallel transport in general relativity in the framework of a manifold, and parallel transport in the algebra of quantum fields in the framework of continuous Lie groups. Is this parallel an accident? Is there a deeper level of grammar? The answers to these questions are not easily found in popular QFT texts, nor in books on the mathematics of differential geometry, group theory, or algebraic topology. In fact, most books purportedly treating these areas of mathematics for the physicist also fail to deliver the deeper grammar.
To get a better grasp of the algebra used in fields and particles, I recommend:
Lie Groups, Lie Algebras, and Some of Their Applications, R. Gilmore, Dover, was originally published in 1974. In the same sense that the two books on the calculus of variations, Elsgolc 1961, and W. Yourgrau and S. Mandelstam 1968 provide the fundamental least action underpinnings of classical and quantum physics, Gilmore provides the foundations to the prescriptions in standard QFT books. The physicist’s book, “Lie Algebras In Particle Physics, From Isospin to Unified Theories,” 2nd ed., H. Georgi makes a ton more sense after Gilmore. If I had stumbled across Gilmore sooner, I probably wouldn’t have spent years pouring over a ton of pure mathematics texts, never quite understanding how to bridge pure algebraic topology back to quantum fields. The following books should probably be read in reverse order from the way I found and read them. They are:
Groups, Representations And Physics, 2nd ed., H. F. Jones, Institute of Physics Publishing. This was the first book that took me a long way into both understanding and being able to apply group theoretic methods to quantum mechanics and quantum fields. After working through Jones, however, I still felt there was a deeper plane of truth, or a better grammar if you will. There was still too much “genius”, too much particularization. Before reading Jones, I recommend as a minimal prerequisite an introductory text on group theory at the Schaum’s outline level. I personally like, “Modern Algebra, An Introduction”, 2nd ed., J. R. Durbin, Wiley. You need only cover the material up through group theory. Take with you the notion of a normal subgroup when you proceed to read Gilmore.
Lie Algebras In Particle Physics, From Isospin to Unified Theories, 2nd. ed., H. Georgi, Frontiers in Physics. I couldn’t have read this book without first having read and worked through Jones. Georgi was difficult for me, but when I cracked it, I began to feel like I was starting to understand the physicist instead of the mathematician. Ideally, read the first four chapters of R. Gilmore’s text first. The 5th chapter covers applications to areas typically presented in graduate physics coursework. Then read Jones, then Georgi. There will be much less for you to have to accept by fiat.
To understand gauge potentials is QFT, look at:
Geometry, Topology and Physics, M. Nakahara, Graduate Student Series in Physics, chapter I read the first four chapters before skipping to chapter 9. To me, chapter 9 seems fairly self-contained. However, by the time I happened upon Nakahara, my background in mathematics was far beyond my 36 hour masters degree in pure mathematics, and I also knew what the goal was beforehand thanks to another book, namely, “Topology, Geometry, and Gauge Fields, Foundations,” G. L. Naber. Naber sucks. Naber is part of the reason I overdid mathematics, but Naber put the goal, the mature grammar in easy to understand words. “…These Lie algebra-valued 1-forms…are called connections on the bundle (or, in the physics literature, gauge potentials).” The gauge fields in QFTs are connections over principle bundles. If anything, you have to read Naber’s chapter 0 for motivation, and I’ve reluctantly come to appreciate all of the mathematics I studied trying to get through Naber, especially differential forms. At this point I began to see that there is probably no end to physics theoreticians cooking up hypothetical universes that don’t necessarily have to have anything to do with what we perceive to be our universe. Even theorizing over our own apparent universe is probably unlimited. The creative degrees of freedom to cook up mathematical universes that behave at low energy like what we observe seem infinite. As our experimental knowledge grows, we exile certain theories of physics into the realm of mathematics, only to quickly create a whole new frontier of endless physics-based possible universes. This realization took the wind out of my pursuing my belief in Einstein’s dream of a final theory. By the way, I found a pretty tidy review of differential forms online, namely, “Introduction to differential forms,” D. Arapua, 2009. I was never satisfied by any of the physics books purportedly written to teach forms.
I actually reviewed a path of books/literature/key physics ideas/key math methods from junior physics texts to postgraduate books at
https://www.physicsforums.com/showthread.php?t=540829
Hope this is useful,
Alex