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

• URL: http://arxiv.org/abs/2302.11666v1
• Date: Wed, 22 Feb 2023 21:42:58 GMT
• Title: Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Authors: Jean Alexandre, Madeleine Dale, John Ellis, Robert Mason, Peter Millington
• Abstract summary: There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians. This Letter provides such a formulation, which relies crucially on the ability to span the state space in such a way as to the same positive-definite inner product.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 mention possible applications to the oscillations of mesons and neutrinos.

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