Complexified quantum field theory in operator form

TL;DR

This paper introduces a novel operator-based formalism for quantum field theory that avoids common mathematical issues and provides a new gauge condition for electromagnetic fields, with potential applications to quantum gravity.

Contribution

It develops a complexified operator formalism for quantum fields and proposes a new gauge condition for electromagnetic fields, enhancing the theoretical framework for multicomponent fields.

Findings

Formalism is free of many mathematical issues of standard quantum field theory

New gauge condition describes absence of scalar and longitudinal photons

Framework is suitable for multicomponent fields including quantum gravity

Abstract

The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This formalism, being free of many dubious mathematical situations characteristic to the standard treatment of quantum fields, is applied in formulation of the new gauge condition for electromagnetic field that describes the absence of the scalar and longitudinal photons. Proposed formalism offers adequate theoretical framework for proper description of the multicomponent fields, including quantum gravity.