Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry

TL;DR

This paper develops a method to construct PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry, demonstrating their potential for consistent quantum probabilistic interpretation despite symmetry breakdowns.

Contribution

It provides a closed-form integrability approach for CPT-symmetric Hamiltonians and embeds them in a supersymmetric framework, expanding understanding of non-Hermitian quantum systems.

Findings

Constructed CPT-symmetric non-Hermitian Hamiltonians with a closed-form method

Showed these Hamiltonians can have a consistent probabilistic interpretation

Analyzed the mathematical consistency of the construction

Abstract

Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the Hamiltonians in a supersymmetric scheme is achieved. For a particular choice of the interactions the rigorous mathematical consistency of the construction is scrutinized suggesting that quantum systems with non-self-adjoint Hamiltonians may admit probabilistic interpretation even in presence of a manifest breakdown of both T symmetry (i.e., Hermiticity) and PT symmetry.