Questions tagged [wightman-fields]
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How are point-dependent concepts such as correlation functions, renormalization, cluster decomposition...etc interpreted in axiomatic QFT?
In traditional quantum field theory we often speak about things happening at a point. For example, the correlation function
$$\langle 0 | \phi(x) \phi(y)\ | 0\rangle \tag{1}$$
can be thought of the ...
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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 ...
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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 ...
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How are Schwinger and Wightman functions used in practice?
In Reed & Simon's Methods of Mathematical Physics Volume II, they define a (Hermitian scalar) quantum field theory to be the quadruple $\langle \mathcal{H}, U, \varphi, D\rangle$ that satisfies ...
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Can quantum fields be smeared in space (rather than spacetime)?
I am interested in what is known about the possibility of smearing interacting quantum fields on a Cauchy slice. This is easy to do for free fields and their conjugate momentum, and indeed this is ...
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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 ...
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Help with Green functions of Wightman fields
I am trying to prove equation 97 in Chapter I of Zavialov's "Renormalized Quantum Field Theory" book, the statement claims that the Green functions of Wightman fields $\check{\phi}$, defined ...
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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 ...
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Fock space and the GNS construction of a free field
Let's consider a scalar field obeying Wightman's axioms. In the Wightman reconstruction theorem, we can reconstruct the Hilbert space by starting with the algebra
$\mathcal{A} = \bigoplus_{n=1}^\infty ...
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How to analytically continue Schwinger functions?
To get Wightman functions $W(t_1, \dots, t_{k-1})$ from Schwinger functions $S(\tau_1 = i t_1, \dots)$, we use analytical continuation.
But I don't think this is simply an issue of plugging $it_a$ for ...
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Wightman functions in quantum field theory
(Source of the 'theorem': click) Given a field $\Phi(x)$ with spin $s$ and its adjoint $\Phi^*(x)$, define the expectation values
\begin{align}
f(x-y)&:=\langle v,\Phi(x)\Phi^*(y)v\rangle, \\ ...
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Are propagators in QFT Wightman Functions?
I am studying relativistic quantum mechanics and I can't really understand how propagators arise from the theory.
They are generally defined as the Wightman function
$$
W_F (t',\vec{x}', t,\vec{x}) \...
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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 ...
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How to show time evolution operator obeys causality?
If we are given a time evolution function $K_t(\phi,\phi')$ which give the amplitude for a field starting in confiruation $\phi$ to go to configuration $\phi'$ after time t. What is the condition that ...
user84158
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Continuity of $\phi(f)\vert\Omega\rangle$ in Wightman QFT
I have to prove the following statement:
$f\mapsto \phi(f)\vert\Omega\rangle$ is continuous, where $\phi$ is a scalar Wightman quantum field, $\Omega$ the vacuum state of the theory and $f$ a ...
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