Questions tagged [quantum-field-theory]

Use this tag for questions about quantum field theory in theoretical/mathematical physics. Quantum Field Theory is the theoretical framework describing the quantization of classical fields allowing a Lorentz-invariant formulation of quantum mechanics. Associate with [tag:mathematical-physics] if necessary.

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52 views

In what situations are Path Integrals well-defined?

In physics I have come across contexts where apparently path integrals are well-defined, and others where they are not. However I have no clear understanding of when and why they succeed or fail to be ...
45 views

Introduction to representation theory? [closed]

I’m studying quantum field theory and have reached the point where I need to understand representation theory for a deeper understanding (specifically for why certain equations give spin-0, 1/2, and 1 ...
16 views

Transformation of line element in Minkowski space under infinitesimal coordinate variation

I'm trying to understand the following problem: We are looking at an infinitesimal coordinate transformation $$x^\mu \rightarrow x^\mu + \epsilon u^\mu(x), \space \epsilon \rightarrow 0$$ and we are ...
58 views

Understanding gauge transformations and relation to Lie Groups?

I am starting to study gauge theory. I have a background in basic group theory, multivariable calculus, and the idea of symmetry in relation to group theory. I am trying to understand why the ...
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Name of the proceedure used to obtain the Dirac equation?

What follows below is a brief description of the procedure Dirac used to obtain the Dirac equation. For my question, which is about this procedure, see the last paragraph. Historically, Dirac was ...
12 views

Complete characterization of local monomials

I'm reading Zavialov's book on QFT and there's a statement there, that I was interested in finding out how to prove. The statement is as follows: If $[A(x), j_{\{\lambda\}}(y)]=0$ for $(x-y)^2<0$ ...
53 views

QFT: Interacting Lagrangian and associated Momentum Space Formulas

Consider a real scalar field with the free part of the Lagrangian $L_0 = −\frac12(\partial \varphi)^2 - \frac12(m^2 \varphi^2),$ and an interaction term $L_1 = \frac12g(φ^2)$. What are the momentum-...
57 views

Formula for calculating symmetry factors for Feynman diagrams?

In a homework exercise for a QFT course I'm taking, we have been tasked with calculating the integral $$Z(g)=\int_{-\infty}^{+\infty} dx\, e^{-\frac{1}{2}x^2 + \frac{g}{3!}x^3}$$ up to order $g^4$ ...
16 views

Following a calculation of entropy in the first quantization scheme

I'm trying to follow the computations of example 5.1 in this paper. To begin with they have a symplectic Hilber space $(\mathcal{K},\tau,\sigma)$, where $(\mathcal{K},\tau)$ is a separable Hilbert ...
38 views

Motivation behind the conjugate Schrödinger equation

What is our motivation behind the conjugate Schrödinger equation (SE), mathematically a conjugate complex scalar is a "projection" of that complex scalar on its opposite quadrant. But what's ...
I am attempting to understand the normalization of one-particle state $|\textbf{p}\rangle \propto a_{\textbf{p}}^\dagger$ in the context of Klein-Gordon field quantization from Peskin & Schroder's ...