Domain wall between the Dirac sea and the "anti-Dirac sea"

TL;DR

This paper investigates the properties of a domain wall separating regions with different Dirac sea fillings in a gravity-Dirac field theory, highlighting the existence of a boundary between states related by PT symmetry.

Contribution

It introduces the concept of a domain wall between the Dirac sea and anti-Dirac sea states, expanding understanding of discrete symmetry effects in gravity-fermion systems.

Findings

Existence of domain walls between different Dirac sea fillings.

States related by PT symmetry have identical energies.

Potential implications for gravitational and quantum field theories.

Abstract

It was shown in work \cite{vergeles2021note} that in the theory of gravity coupled with the Dirac field, each state $|\lambda\rangle$ has its own twin $|\lambda;PT\rangle$, which is obtained by a discrete PT transformation. If in the state $|\lambda\rangle$ the Dirac sea is filled, then in the state $|\lambda;PT\rangle$ there is an "anti-Dirac" filling (in terms of the state $|\lambda\rangle$). It is important that the energies of these states are the same. Therefore, there may be domains with different filling of the Dirac sea. Here we study a domain wall connecting two such adjacent domains.