Axiomatic field theory and Hida-Colombeau algebras

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 defined Hamiltonians are written using ordinary products of interacting scalar fields that are represented as generalised operators on simplified Hida-Colombeau algebras.

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