Dirac Sea for Bosons II -- Study of the Naive Vacuum Theory for the Playground World Prior to Filling the Negative Energy Sea --

TL;DR

This paper explores a naive second quantization approach for bosons analogous to the Dirac sea for fermions, revealing CPT-symmetry breaking but satisfying a related theorem, serving as a theoretical playground rather than a physical model.

Contribution

It introduces and analyzes a naive second quantization of bosons with negative energies, highlighting its symmetry properties and theoretical implications.

Findings

Naive quantization breaks CPT-symmetry.

The theory obeys a modified CPT-like theorem.

Fock space is indefinite, limiting physical applicability.

Abstract

We use our previous idea, in which at first we perform a naive second quantization of both negative and positive energy for the Klein-Gordon equation analogous to the unfilled Dirac sea for fermions, to study as a playground this naive second quantization theory. It is not to be taken seriously physically in as far as it has indefinite Fock space, but it has nevertheless interesting possibilities: Although the naive (quantization) theory represents a spontaneous breakdown of the usual CPT-symmetry, we shall show that it obeys a certain replacement for the CPT-theorem for which a proof is presented in detail.