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6
votes
1answer
198 views

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 ...
4
votes
0answers
62 views

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 ...
3
votes
1answer
119 views

partition function for Wightman and Haag-Kastler QFT

From what I hear, some modern mathematical approach quantum field theory uses the following definition "A $d$-dimensional $S$-structured quantum field theory $Q$ is a mathematical object, ...
3
votes
3answers
150 views

QED as a Wightman theory of observable fields? With a collision theory?

[Note: I'm using QED as a simple example, despite having heard that it is unlikely to exist. I'm happy to confine the question to perturbation theory.] The quantized Aᵘ and ψ fields are non-unique ...
1
vote
1answer
87 views

Error in Kac's “Vertex algebra for beginners” proof that a Wightman QFT gives rise to a vertex algebra?

Given $$ i[Q_k,\Phi_a(x)]=((x_0^2-x_1^2)\partial_{x_k}-2\eta_k x_k E - 2\Delta_a \eta_k x_k) \Phi_a(x), \quad (1.1.8) $$ applying a coordinate change $t= x_0-x_1$, $\bar{t}= x_0+x_1$ and defining $$ ...