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, ...
[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 ...
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 ...