An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass

TL;DR

This paper develops an algebraic PT-symmetric quantum theory incorporating a maximal mass, extending non-Hermitian quantum frameworks with potential experimental implications.

Contribution

It introduces a novel algebraic approach to PT-symmetric quantum theory with a maximal mass, building on and extending previous geometric and non-Hermitian quantum theories.

Findings

Construction of new scalar products for non-Hermitian Hamiltonians

Development of algebraic relativistic pseudo-Hermitian quantum theory

Discussion of experimental investigations related to the theory

Abstract

In this paper we draw attention to the fact that the studies by V. G. Kadyshevsky devoted to the creation of the which \emph{\emph{to the geometric quantum field theory with a fundamental mass}} containing non-Hermitian mass extensions. It is important that these ideas recently received a powerful development in the form of construction of the non-Hermitian algebraic approach. The central point of these theories is the construction of new scalar products in which the average values of non-Hermitian Hamiltonians are valid. Among numerous works on this subject may be to allocate as purely mathematical and containing a discussion of experimental results. In this regard, we consider as the development of algebraic relativistic pseudo-Hermitian quantum theory with a maximal mass and experimentally significant investigations are discussed