Questions tagged [wightman-fields]
35 questions
14
votes
1 answer
What is a precise mathematical statement of the Yang-Mills and mass gap Clay problem?
I am a mathematician writing a statement of each of the Clay Millennium Prize problems in a formal proof assistant. For the other problems, it seems quite routine to write the conjectures formally, but I am having difficulty stating the problem on…
Thales
- 141
13
votes
1 answer
Is it known whether Wightman's axiomatic QFT is logically equivalent to Osterwalder–Schrader's axiomatic QFT?
Constructive QFT has provided some interesting models for dimension $d < 4$ of space-time, satisfying specific axiomatic versions of QFT. On the other hand, it is a well known fact that an axiomatic theory can admit more than one model, the question…
Davius
- 1,700
8
votes
0 answers
Existence of Schwinger Functions for QCD?
It seems to me the 'naive' approach to proving the existence of Yang-Mills in a rigorous context (via Osterwalder-Schrader $\to$ Wightman axioms), would be:
Study gauge invariant lattice QCD correlation functions such as
$$\langle…
QCD_IS_GOOD
- 7,145
8
votes
2 answers
Wilson loop operator in electrodynamics
I'm trying to prove that the Wilson loop operator is well-defined in non-interacting quantum electrodynamics without matter, that is, $\hat{W}(\gamma)$ is a bounded operator on the Hilbert space.
Since the Wilson loop is an exponentiation
$$…
Prof. Legolasov
- 16,527
8
votes
1 answer
Asymptotic Completeness, generalized free fields, and the relationship of thermodynamics with infinity
Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of continuous mass distributions $\rho_n(k^2)$ that…
Peter Morgan
- 10,016
6
votes
2 answers
What is an operator-valued distribution?
I am a mathematician who is trying to understand Wightman axioms.
I do not understand what an operator-valued distribution is, because in this context people say that operators can be unbounded, and as far as I know, unbounded operators do not have…
Nicolò Cavalleri
- 283
5
votes
1 answer
Existence of the S-matrix in AQFT
I am reading the book "An introduction to Symmetry and Supersymmetry in Quantum field theory" by Lopuszanski, and I have some problems understanding his argumentation about the existence of the S-matrix. On page 102 he says
'Both fields,…
S.Farr
- 339
5
votes
2 answers
Extending Wightman axioms to gauge theories
I understand that Wightman axioms were defined for scalar quantum field theories. However, what prevents axiomatization of non-scalar quantum field theories, such as gauge theories, even for free field?
michelav
- 133
5
votes
1 answer
Wightman's theorem, in terms of time-ordered functions$.$
According to Wightman's theorem, given a set of distributions $\{W_n\}$ satisfying a set of axioms, we may conclude the existence of a set of operators $\{\phi\}$ which satisfy some properties, and such…
AccidentalFourierTransform
- 56,647
5
votes
0 answers
Axiomatic QFT: Time-slice Axiom vs Transformation Properties
I am studying Wightman axioms and Haag–Kastler axioms for QFT from Haag's book "Local Quantum Physics". In both axiomatic frameworks, he introduces the "Time-slice Axiom" (axiom G) as
"There should be a dynamical law which allows one to compute…
user108500
4
votes
0 answers
Renormalisation in rigorous algebraic formulation of QFT
Before I get to the point, let me quickly describe the context and what level of understanding I’m trying to achieve, if possible. I’d like to get some intuition on more rigorous approaches of QFTs, how they relate to “standard textbook perturbative…
4
votes
1 answer
What is the field map in 0+1-dimensional QFT?
I'm a beginner trying to learn something about the Wightman axioms. I got the idea that from an abstract Hilbert space and an abstract Hamiltonian operator, I should be able to produce a trivial example of a "0+1-dimensional Wightman quantum field…
Upasker
- 120
- 4
4
votes
3 answers
Wightman quantum field - Interpretation
I have a question regarding the interpretation of the Wightman quantum field in mathematical quantum field theory.
A quantum field $\phi$ is a operator-valued distribution. This means that $\phi$ is a linear…
user228212
4
votes
1 answer
Wightman distributions
According to the Wightman axioms, for Wightman fields $\phi_1,\dots,\phi_n$, the vacuum expectation value
$$\langle\Omega, \phi_1(f_1)\dots\phi_n(f_n)\Omega\rangle$$
is a multilinear continuous map from an n-tuple product of Schwartz spaces to the…
user353840
- 327
4
votes
0 answers
Glimm and Jaffe's paper on the construction of 2D QFTs
I am presently interested in the construction of low-dimensional (2D/3D) QFTs where all the Wightman axioms have been proved and to this end, I started reading this article, which is recommended in this discussion.
The article looks interesting but…
IchKenneDeinenNamen
- 121
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