Introduction to quantum field theory exhibiting interaction

TL;DR

This paper introduces a revised framework for constructing interacting relativistic quantum fields within Hilbert spaces, aligning with physical axioms and matching Feynman series results for scattering cross sections.

Contribution

It presents a new approach that relaxes the Hermitian operator assumption, enabling explicit construction of interacting quantum fields satisfying key physical axioms.

Findings

Real scattering cross sections match Feynman series predictions

Framework satisfies local commutativity and relativistic invariance

Eliminates the need for Hermitian operator assumption

Abstract

This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical spacetimes. The local commutativity, relativistic invariance, positive energy and Hilbert space realization axioms are satisfied. The revision eliminates conjecture that a real quantum field is necessarily a Hermitian Hilbert space operator. The resulting explicit scattering cross sections coincide with the first contributing order from Feynman series for a neutral scalar field.