The Dirac Equation in the Model With a Maximal Mass

TL;DR

This paper explores the Dirac equation within a model featuring a maximal mass M using anti de Sitter space, demonstrating that both free and interacting Hamiltonians are pseudo-Hermitian, enabling a consistent quantum theory.

Contribution

It introduces a framework where the Dirac equation in a maximal mass model is shown to have pseudo-Hermitian Hamiltonians, allowing for a consistent quantum theory.

Findings

Hamiltonians are pseudo-Hermitian in the model

Consistent quantum theory can be constructed using pseudo-Hermitian rules

Results align with those obtained from the ordinary Dirac equation

Abstract

In paper within the model with a maximal mass M and with use of anti de Sitter space is considered the Dirac equation properties for a fermion of mass m on the mass surface. The paper shows that free Hamiltonian and Hamiltonian with interaction are pseudo-Hermitian. If we accept the appropriate rules of use of pseudo-Hermitian Hamiltonians, we can construct the consistent quantum theory with final results obtained using the ordinary Dirac equation.