Axiomatic field theory and Hida-Colombeau algebras

TL;DR

This paper develops an axiomatic quantum field theory framework using generalized operators within Hida-Colombeau algebras, enabling rigorous formulation of interacting scalar fields and Hamiltonians.

Contribution

It introduces a novel approach combining axiomatic QFT with Hida-Colombeau algebras for rigorous operator products and derivatives.

Findings

Representation of operators in Hida-Colombeau algebras.

Rigorous formulation of Hamiltonians for interacting fields.

Mathematically consistent products and derivatives of quantum fields.

Abstract

An axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of the fields in simple and mathematically rigorous ways. Various spaces are explored for representation of these operators with this exploration culminating with a Hida-Colombeau algebra. Rigorous well defned Hamiltonians are written using ordinary products of interacting scalar fields that are represented as generalised operators on simplified Hida-Colombeau algebras.