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arXiv · 2302.11666

Oscillation probabilities for a PT-symmetric non-Hermitian two-state system

Jean Alexandre·Madeleine Dale·John Ellis·Robert Mason·Peter Millington
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Abstract

There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians, but a formulation of transition matrix elements consistent with positivity and perturbative unitarity has so far proved elusive. This Letter provides such a formulation, which relies crucially on the ability to span the state space in such a way that the interaction and energy eigenstates are orthonormal with respect to the same positive-definite inner product. We apply this non-Hermitian approach to two-neutrino flavour oscillations, and show how it can accommodate the seesaw mechanism.

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Jean Alexandre, Madeleine Dale, John Ellis, Robert Mason, Peter Millington. 2023-02-22. Oscillation probabilities for a PT-symmetric non-Hermitian two-state system. https://doi.org/10.1088/1751-8121/ae2700

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