Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866908836846108672 |
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| author | Alexandre, Jean Dale, Madeleine Ellis, John Mason, Robert Millington, Peter |
| author_facet | Alexandre, Jean Dale, Madeleine Ellis, John Mason, Robert Millington, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Oscillation probabilities for a PT-symmetric non-Hermitian two-state system Alexandre, Jean Dale, Madeleine Ellis, John Mason, Robert Millington, Peter Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Oscillation probabilities for a PT-symmetric non-Hermitian two-state system |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2302.11666 |