The challenge of non-hermitian structures in physics

TL;DR

This paper reviews the challenges and open problems associated with non-Hermitian Hamiltonians and indefinite Hilbert spaces in physics, highlighting the need for consistent physical interpretations.

Contribution

It provides a concise overview of physical systems involving non-Hermitian structures and discusses the unresolved issues in their physical interpretation.

Findings

Non-Hermitian Hamiltonians appear in various physical contexts.

The interpretation of indefinite Hilbert spaces remains an open problem.

Pseudo-Riemannian manifolds in GR are exceptions with established interpretations.

Abstract

We present a brief review of physical problems leading to indefinite Hilbert spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian manifolds in GR, the problem of a consistent physical interpretation of these structures still waits to be faced. In print in Rev. Mex. Fis.