Questions tagged [quantum-field-theory]

Question 1

I apologize for the vague question, but I'm genuinely curious about whether research is still being done on distribution theory---is it a well-established tool or are there still relevant open ...

Question 2

On the symmetrized (bosonic) Fock space $\mathcal F_{\mathcal B}$, the standard creation and annhilation operators are defined by \begin{align*} A^{\dagger}(e_k) |\, n_1,n_2,...,n_k,... \rangle & ...

Question 3

In quantum field theory, n-point functions $\langle\text{vac}|T\phi(x_1)...\phi(x_n)|\text{vac}\rangle$ are computed to represent the scattering amplitudes in particle physics. These n-point functions ...

Question 4

I'm dealing with a mathematical problem stemming from quantum field theory (QFT). However, at the moment, I'm not concerned with the physics aspect of it and, hence, I wish to view it in purely formal ...

Question 5

All the reference I found on the Gaussian Free Field focus alternatively on a lattice setting (e.g. the book of Friedly & Velenik) or on a continuum setting in finite volume (e.g. the notes of ...

Question 6

For this one loop integral, I have approached it using Feynman Parametrization, $$\int_{}^{}\frac{d^{d}k}{(2\pi)^{d}}\frac{1}{(k^{2}+m_{1}^{2})[(k-q)^{2}+m_{2}^{2}]}$$ The parametric integral that I ...

Question 7

I am confused about the definition and usage of quantum field in Talagrand's book What is a Quantum Field Theory. On page 133, it is said that Massive scalar free quantum field is the map $\phi: \...

Question 8

I'm going through Streater & Wightman's PCT and spin-statistics book and am thinking about section 2-4 on tubes and extended tubes. For simplicity I'll consider the case of $\mathbb C^4.$ We begin ...

Question 9

I am asking this question on MSE first because I believe my question is all about mathematical clarification; if the community believes this post should migrate to PSE, by all means. The setting is ...

Question 10

Dear users of Stack Exchange, Feynman’s Theorem is stated as Theorem 3.5 in “Mathematical Ideas and Notions of Quantum Field Theory” by Pavel Etingof. These notes are freely available through both MIT ...

Question 11

I am trying to compute the following loop integral: $$ \require{cancel} \displaystyle I= \int \frac{d^4k}{(2\pi)^4}\bar u(p')\frac{[k^2k^\mu - (k\cdot p)\cancel{k}\gamma^\mu -(k\cdot p')\gamma^\mu\...

Question 12

I am considering the $\phi^3$ theory in $d = 3$ dimensions. The propagator is given by the following formula $$ G(p^2) = \frac{-i}{p^2 + m_0^2 + M^2(p^2) - i\epsilon} $$ where $$ M^2(p^2) = -\frac{g_0^...

Question 13

I am trying to evaluate the following integral over $d$-dimensional momentum: $$ \int \frac{d^d p}{(2\pi)^d} \frac{p^\mu}{(p^2 + \Delta^2)^b} $$ Is there any trick I can use? For instance, if $p^\mu$ ...

Question 14

Let us define the function $\mathcal G: \mathbb R\to\mathbb R$ as the antiperiodic continuation of: $$ \mathcal G(x) = \sum_{p=1}^P \alpha_p \frac{\exp(-\epsilon_p x)}{1 + \exp(-\epsilon_p)}, \quad ...

Question 15

I am just studying the Dirac algebra in 4D spacetime composed of four $n\times n$ gamma matrices $\{\gamma^\mu\}=\{\gamma^0,\gamma^1,\gamma^2,\gamma^3\}$ satisfying the following anticommutation ...

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Questions tagged [quantum-field-theory]

Is there still active research in the mathematical theory of distributions?

Are the $\sqrt n$ prefactors "natural" in creation/annihilation operator definitions?

n-point functions as generalized Hilbert-Schmidt kernels

Symmetrization of functional derivatives

Gaussian-free-field and infinite volume

Parametric Integral Analytic Solution

Clarification of definition of quantum field in Talagrand's book

Analytic Continuation of Representation of Lorentz Group (Streater and Wightman).

Precise mathematical meaning of superselection rules

Can Feynman’s Theorem be proved without Wick’s Theorem?

Feynman parametrization goes wrong

Determining Discontinuity Across Branch Cuts for $\phi^3$ propagator

How to Evaluate this Integral Over Lorenzian Momentum Space

Bounding the determinant of a matrix which samples a sum of exponentials

Basis of the Dirac algebra

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