Is quantum field theory a generalization of quantum mechanics?

TL;DR

This paper introduces a mathematical model generalizing quantum mechanics to quantum field theory concepts, replacing operator ordering with Weyl-Moyal algebra, aiding proofs of quantum field theory results without relying on physical interpretations.

Contribution

It presents a novel mathematical framework that extends quantum mechanics to quantum field theory using path integrals and Weyl-Moyal algebra, bypassing traditional physical notions.

Findings

Model reproduces quantum field theory results mathematically

Provides a new tool for proving quantum field theory theorems

Facilitates translation of results into standard quantum field theory language

Abstract

We construct a mathematical model analogous to quantum field theory, but without the notion of vacuum and without measurable physical quantities. This model is a direct mathematical generalization of scattering theory in quantum mechanics to path integrals with multidimensional trajectories (whose mathematical interpretation has been given in a previous paper). In this model the normal ordering of operators in the Fock space is replaced by the Weyl-Moyal algebra. This model shows to be useful in proof of various results in quantum field theory: one first proves these results in the mathematical model and then "translates" them into the usual language of quantum field theory by more or less "ugly" procedures.