Non-Hermitian Heisenberg representation

TL;DR

This paper develops a non-Hermitian version of quantum mechanics within the Heisenberg representation, paralleling recent advances in the Schrödinger form, and explores its theoretical foundations.

Contribution

It introduces a novel non-Hermitian Heisenberg representation, expanding the framework of non-Hermitian quantum mechanics beyond the Schrödinger picture.

Findings

Establishment of a non-Hermitian Heisenberg framework

Parallelism with non-Hermitian Schrödinger representation

Theoretical demonstration of the new formalism

Abstract

In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated that it is also possible to construct an analogous non-Hermitian version of quantum mechanics in its Heisenberg representation.