Hi guys. So I just finished most of Griffith's Introduction to QM text (including the problems). I was wondering, is this text enough to delve into Srednicki's Quantum Field Theory text or should I also go through Shankar's Principles of QM? Relativity should not be an issue (I hope) as I have knowledge of it at the level of Carroll's Spacetime and Geometry text. Thanks in advance.
I personally find David Tong's notes to be more understandable than any QFT text: http://www.damtp.cam.ac.uk/user/tong/qft.html I guess you can (and should) supplement this notes with textbooks and try to see if you can understand the subject... if not, then just pick up the necessary pre-requisites along the way!
Srednicki is a very steep climb. In addition to the other books mentioned, I recommend Aitchison & Hey. There's also Griffith's own particle physics text.
If all you have is Griffith's, I'd suggest at least using Shankar as a reference. You really need to internalize bra/ket notation (and what it implies about vector/function spaces) before you can begin to play around with more field theoretic ideas. The easier the notation is to manipulate, and the more internalized the ideas, the less you'll get hung up on the "normal" quantum mechanical operations. While this next advice is a bit unconventional- get acquainted with the Dirac equation before you start with quantum field theory. Try to solve it for the free particle and the hydrogen atom (it can be solved exactly), and look at some expectation values of operators. I often think we move to quickly from quantum mechanics in a non-relativistic setting to field theory and skip some of the insight that can be gained with Dirac as an intermediate. Shankar (among other books) treats the Dirac equation.
Perhaps this book can smoothen the transition: http://www.amazon.com/Advanced-Quan...=sr_1_1?ie=UTF8&s=books&qid=1305574712&sr=8-1 Part 1 of the books covers 2nd quantization while Part 2 covers Klein Gordon & Dirac equations.
Should a beginner in QFT have very strong math skills or is this math skills gained later during the study?
The David Tong QFT notes previously mentioned should give you a good idea. http://www.damtp.cam.ac.uk/user/tong/qft.html If you've had a year of undergrad QM that used Dirac notation, you should be reasonably prepared. Some math you should already have (like contour integration, but you can learn that in an afternoon from Boas or another "math methods" book), and some is part of learning QFT (e.g. spinors). It's a good idea to have a "math methods" book handy for specific topics like the gamma function.
Thank You , so if I want to do research in QFT or string theory , should I do additional courses in advanced math other than that required by a traditional QFT or string theory and also have very strong skills in math to do research ?
A theoretical physicist needs to be comfortable with abstract mathematics to be able to read the mathematical literature. The math needed for theoretical work is not always explained in a friendly "for physicists" textbook. Unfortunately, you probably won't have time for much additional coursework, so much of this has to be picked up by self-study. Szekeres book may give you the flavor of some of the math involved.