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

Axiomatic field theory and Hida-Colombeau algebras