PT symmetric fermionic particle oscillations in even dimensional representations

• URL: http://arxiv.org/abs/2407.02036v2
• Date: Wed, 02 Oct 2024 18:14:05 GMT
• Title: PT symmetric fermionic particle oscillations in even dimensional representations
• Authors: Leqian Chen, Sarben Sarkar,
• Abstract summary: We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems. The resulting quantum mechanical evolution is shown to be unitary and probability is conserved by the oscillations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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