Time-dependent version of cryptohermitian quantum theory

TL;DR

This paper explores how time-dependent observables in certain quantum models necessitate a dynamic representation of the physical Hilbert space, extending the framework of cryptohermitian quantum theory.

Contribution

It introduces a time-dependent approach to cryptohermitian quantum theory, highlighting the need for a time-dependent Hilbert space representation for certain observables.

Findings

Time-dependent observables require a time-dependent Hilbert space.

Cryptohermitian models can be consistently described with a dynamic Hilbert space.

The approach extends the applicability of cryptohermitian quantum theory.

Abstract

For many quantum models an apparent non-Hermiticity of observables corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.