PT symmetric fermionic particle oscillations in even dimensional representations

TL;DR

This paper introduces a new class of quantum particle oscillations in fermionic systems using PT symmetry and T^2=-1, ensuring unitary evolution and probability conservation in both relativistic and non-relativistic contexts.

Contribution

It presents a novel framework for fermionic particle oscillations based on PT symmetry with T^2=-1, expanding the understanding of quantum dynamics in such systems.

Findings

Oscillations are unitary and probability-conserving.

The framework applies to both relativistic and non-relativistic systems.

A modified CPT inner product ensures consistent quantum evolution.

Abstract

We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The Hamiltonians are chosen at the outset to be self-adjoint with respect to a PT inner product. The quantum mechanical time evolution is based on a modified $CPT$ inner product constructed in terms of a suitable $C$ operator. The resulting quantum mechanical evolution is shown to be unitary and probability is conserved by the oscillations.