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Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.

9 votes
2 answers
3k views

Peskin Schroeder and the general solution to Callan-Symanzik Equation

I have a couple of questions regarding Peskin and Schroeder's derivation of the solution to the Callan-Symanzik equation. First of all, they claim that using $$\int_\lambda^\bar{\lambda}\frac{d\lambda …
9 votes
2 answers
2k views

Proof of Goldstone's theorem

I am reading Matthew Schwartz's wonderful QFT book, but I have stumbled in my attempts to understand his rather brief proof of Goldstone's theorem. The preliminary information is that $$HQ|\Omega\ran …
12 votes
2 answers
5k views

Charge operator action in QFT

I have a quick question regarding the action of the charge operator in quantum field theory. I am reading Schwartz's book on QFT, and he proves the two following commutation relations $$[Q,\psi]=-\psi …
1 vote
0 answers
63 views

Which particles to include in loop corrections to maintain gauge invariance

I have been reading both Peskin and Schröder and Schwartz's QFT books, in particular the sections in each book regarding precision tests of the standard model where they calculate loop corrections to …
6 votes
3 answers
535 views

Why does a perturbative theory imply coupling must be increasing or decreasing?

I am reading some of Schwartz's quantum field theory book, and I have come across a passage I find confusing. It states that When the coupling is small, the theory is perturbative, and then the c …
7 votes
4 answers
2k views

Translational invariance implying diagonal representation in momentum space

I have just come across something in my reading of Peskin and Schroeder that claims that because a function, in this particular case a two-point correlation function, is translationally invariant, it …