On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator

TL;DR

This paper explores the theoretical possibility of negative energies and masses in the Dirac equation, demonstrating that negative energies can be consistent with negative masses via a unitary PT transformation.

Contribution

It introduces a framework where negative energies and masses are compatible in relativistic quantum mechanics using a unitary PT symmetry.

Findings

Negative energies are acceptable with negative masses.

Negative energy and mass anti-fermions relate to positive counterparts through PT transformation.

Provides a new perspective on negative mass and energy in quantum theory.

Abstract

We review the standards of relativistic quantum mechanics such as the Dirac equation under the concept of negative masses. We show that negative energies are acceptable provided the masses are simultaneously negative. Negative energy and mass anti fermions are obtained from positive energy and mass fermions through a unitary PT transformation.