Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism

TL;DR

This paper introduces a generalized vielbein formalism that systematically transforms non-Hermitian quantum Hamiltonians into Hermitian ones by redefining the Hilbert space basis, clarifying the underlying physics.

Contribution

It develops a formalism that converts non-Hermitian Hamiltonians into Hermitian form through a vielbein-like transformation, providing a new perspective on non-Hermitian quantum systems.

Findings

Any non-Hermitian Hamiltonian can be Hermitized without changing physical predictions.

The formalism clarifies the physical interpretation of non-Hermitian systems.

The approach offers a systematic way to analyze non-Hermitian quantum models.

Abstract

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering the induced Hamiltonian to be Hermitian. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics. Thus we show how to find a reference frame (corresponding to Einstein's quantum elevator) in which a non-Hermitian system, equipped with a non-trivial Hilbert space metric, reduces to a Hermitian system within the standard formalism of quantum mechanics.