Twisting factors and fixed-time models in quantum field theory

TL;DR

This paper develops fixed-time quantum field models with non-trivial commutation relations influenced by a twisting factor, linking gauge transformations and Coulomb interactions within a novel framework.

Contribution

It introduces a class of fixed-time models where twisting factors determine the interaction structure and gauge transformations in quantum field theory.

Findings

Twisting factors can be chosen as fundamental solutions of differential operators.

The Coulomb potential as a twisting factor reproduces Coulomb gauge interactions.

The model incorporates local gauge transformations via the bosonic field Laplacian.

Abstract

We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting factor"). If the twisting factor is fundamental solution of a differential operator, then applying the differential operator to the bosonic field yields a generator of the local gauge transformations of the Dirac field. Charged vectors generated by the Dirac field define states of the bosonic field which in general are not local excitations of the given reference state. The Hamiltonian density of the bosonic field presents a non-trivial interaction term: besides creating and annihilating bosons, it acts on momenta of fermionic wave functions. When the twisting factor is the Coulomb potential, the bosonic field contributes to the divergence of an electric field and its Laplacian generates local gauge transformations of the Dirac field. In this way we get a fixed-time model fulfilling the equal time commutation relations of the interacting Coulomb gauge.