Questions tagged [quantum-field-theory]
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.
14,503 questions
3 votes
1 answer
80 views
Interpretation of real scalar field, its propagator and causality [duplicate]
It seems this has been discussed here previously (e.g this and this post), but I still feel uneasy. Essentially, I think it all boils down to the popular interpretation of the scalar field operator in ...
- 1,158
2 votes
1 answer
70 views
Expressing Feynman Integrals Using Schwinger Parameterization
I am trying to practice the techniques given in the book "Feynman Integrals: A Comprehensive for Students and Researchers," by Stefan Weinzierl (preprint). I am getting stuck on one point ...
5 votes
0 answers
127 views
Structure of Higgs potential
The Higgs potential is written as $V(\phi) = -\mu^2 |\phi|^2 + \lambda^2 |\phi|^4$, where $|\phi|^2 = \phi^\dagger \phi $ and $ \phi $ is a complex scalar doublet. My question is: why do we not ...
- 51
1 vote
0 answers
89 views
Dyson series expression for the two-point Green function
On Chapter 7 of Fetter & Walecka, the authors prove Dyson formula for the (imaginary time) propagator $U(t,t_{0}) = e^{H_{0}t_{0}}e^{-H(t_{0}-t)}e^{-H_{0}t}$, where I am ommitting the $\hbar$'s. ...
- 251
0 votes
0 answers
47 views
Sign in the PCAC relation and consistency with the GMOR relation
In Peskin & Schroeder (Eq.~(19.88)), the PCAC matrix element is written as $\langle 0| j^{\mu 5 a}(x) | \pi^b(p) \rangle = -\, i\, p^\mu f_\pi\, \delta^{ab}\, e^{-ip\cdot x}.$ Q1. Where does this ...
- 23
6 votes
1 answer
212 views
Why do these first-order diagrams represent "direct" and "exchange" interactions?
In Quantum Theory of Many Particle Systems by Fetter and Walecka, they perturbatively expand the fermionic interacting single particle Green's function $iG_{\alpha\beta}(x, y)$ (where $\alpha$, $\beta$...
- 157
3 votes
2 answers
61 views
Scattering probability distribution for $2 \rightarrow 2$ scattering
Consider a 2-to-2 particles scattering process (treated in second quantization) of particles with the following $4$-momenta: $$p_1 + p_2 \rightarrow p_3 + p_4.$$ The probability measure associated ...
- 476
13 votes
4 answers
2k views
Why does QED use spinors but Classical Electrodynamics doesn't?
I am curious as to why we find Dirac spinors in QED but when working in CED we can formulate systems using complex scalar fields. For instance, the typical Lagrangian density for a charged particle ...
- 2,638