Questions tagged [quantum-field-theory]
For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.
378
questions
8
votes
2
answers
314
views
On the $\phi^4$-model on infinite lattice
It is mentioned in this answer Is there a program to solve The Yang–Mills Existence and Mass Gap problem similar to the Hamilton's program to solve Poincaré Conjecture?
that it is an open ...
10
votes
1
answer
496
views
About Friedrichs historical contribution to QFT cited in Reed and Simon
In the Reed and Simon book, Appendix X.7, they mention that Friedrichs provided the first examples of inequivalent representations of the canonical commutation relations via the Weyl relations in the ...
0
votes
0
answers
41
views
Status of generalization of timelike tube theorem to algebras of causal completions
The timelike tube theorem states that the additive algebra $A_{\text{add}}(U)$ of operators in a spacetime region $U$ is equal to the additive algebra $A_{\text{add}}(E(U))$ of the timelike envelope $...
0
votes
1
answer
127
views
Gauge invariance issues of YM theories in 2D Euclidean space
In order to be clear, I will write down every component explicitly. Also, I assume Euclidean metric in this post, so that spacetime indices are written as $i,j$ rather than $\mu, \nu$.
Following Wiki, ...
0
votes
1
answer
91
views
Extracting each field operator as Wightman fields from a set of time-ordered products satisfying Eckmann-Epstein axioms
The paper by Eckmann-Epstein proves that Schwinger functions at "coinciding points" uniquely defines "time-ordered products".
In physics, these "time-ordered products" ...
2
votes
0
answers
164
views
Renormalization from cohomology point of view
In order to construct a Euclidean quantum filed theory one usually needs to take care of the renormalization problem. Let us consider a simple model like $\phi^4$ in dimension two. In this case just ...
6
votes
2
answers
258
views
The equivalence of stochastic quantization and path integral quantization
I am looking for a reference in which the equivalence of stochastic quantization and
path integral quantization has been shown. It would be great if I can see such a relation for a Euclidean quantum ...
6
votes
0
answers
128
views
Wick ordering, probability vs physics
Consider a collection of creation $a^\dagger$and annihilation operators $a$. In physics one defines Wick ordering (also known as normal ordering) as a prescription to place all creation operators ...
1
vote
1
answer
250
views
Wick product of free fields and wave front sets in the sense of Lars Hörmander
Let $\phi$ be the neutral, massive and free scalar field in $\mathbb{R}^4$. That is, $\phi$ is a tempered distribution whose values are unbounded operators on the Bosonic Fock space.
Note that the ...
1
vote
0
answers
147
views
Recommendation to understand mean field theorem
I am studying Rodnianski and Schlein - Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics. Everything was clear for me and I reproved everything before inequality (3.22) (except ...
4
votes
1
answer
193
views
Reference request: Gaussian measures on duals of nuclear spaces
I am interested in constructive quantum field theory where Gaussian measures on duals of nuclear spaces (specifically, the space of tempered distribution $\mathcal{S}'(\mathbb{R}^n)$) play a key role. ...
4
votes
4
answers
463
views
Why computing $n$-point correlations?
I am trying to find a sufficiently convincing answer to this question, but it has been taking so much of my time and I can't get anywhere. It also follows my previous question on PSE.
In axiomatic QFT,...
0
votes
0
answers
144
views
Dependence of functional integral on the function space
In physics, the following functional integral is considered
\begin{gather}
Z[J]= \int Df \exp(-\int d^dx( f\Box f+\lambda f^4 +Jf ))
\end{gather}
It is usually said that the integration is performed ...
4
votes
2
answers
228
views
Reference for rigorous interacting many-body quantum mechanics
Are there good references for (both zero and finite time) interacting systems of quantum many-body theory? More precisely, I would be interested in references discussing the following topics:
Second ...
1
vote
0
answers
159
views
AQFT from a Lagrangian
In physics, the fundamental description of physical theories frequently revolves around the concept of a Lagrangian. My expertise encompasses diverse algebraic formulations within the domain of ...