Quantum Dirac field without vacuum energy divergence

TL;DR

This paper introduces a quantum Dirac field theory that eliminates vacuum energy divergences by removing an extra degree of freedom, leading to a divergence-free, consistent fermion-antifermion framework.

Contribution

It presents a novel approach to remove vacuum energy divergences in Dirac fields by constraining an extra degree of freedom, defining a new spin 1/2 field as the antifermion.

Findings

Vacuum energy divergence is eliminated.

A new conservation law relates fermion and antifermion fields.

Charge and current densities are explicitly derived.

Abstract

A quantum Dirac field theory with no divergences of vacuum energy is presented. The vacuum energy divergence is eliminated by removing a extra degree of freedom of the Dirac fields. The conditions for removing the extra degree of freedom, expressed in the form of a conservation law and an orthogonality relation, define another spin 1/2 field with the same rest mass that is just the antifermion field. The anticommutation relations for fermion and antifermion fields are imposed by this conservation law. Both fermion and antifermion fields have only states with positive energies due to the orthogonality relation. The expressions of the charge density and the current density are obtained. The charge conservation law is established. A form for canical quantization applicable to both Boson and Dirac fields is introduced.