Elements of a non-Hermitian quantum theory without Hermitian conjugation - scalar product and scattering

TL;DR

This paper proposes a non-Hermitian quantum framework that maintains Lorentz covariance and analyticity, enabling local and perturbative descriptions of phenomena like confinement and superconductivity without relying on traditional Hermitian conjugation.

Contribution

It introduces a scalar product and scattering formalism in non-Hermitian quantum theory that do not depend on metric or complex conjugation, preserving key physical principles.

Findings

Derived a Lorentz covariant scalar product without metric or conjugation.

Extended scattering theory analytically to non-Hermitian regimes.

Provided a formalism for local, perturbative descriptions of complex phenomena.

Abstract

The descripition of in a Hermitian setting seemingly nonlocal and nonperturbative phenomena like confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena appear perturbative and local. The short presentation provides a clue how this can be done on the basis of Lorentz covariance while preserving the analyticity of the theory. After deriving with the help of Lorentz covariance a quantum scalar product without making any use of metric or complex conjugation we sketch how the formalism of scattering theory can be extended analytically to a non-Hermitian regime.