dorsal/arxiv
View SchemaPT-symmetry and its spontaneous breakdown explained by anti-linearity
| Authors | Stefan Weigert |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209054 |
| URL | https://arxiv.org/abs/quant-ph/0209054 |
| DOI | 10.1088/1464-4266/5/3/380 |
| Journal | J. Opt. B 5 (2003) S416 |
Abstract
The impact of an anti-unitary symmetry on the spectrum of non-hermitean operators is studied. Wigner's normal form of an anti-unitary operator is shown to account for the spectral properties of non-hermitean, PT-symmetric Hamiltonians. Both the occurrence of single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PT. In this framework, the concept of a spontaneously broken PT-symmetry is not needed.
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"abstract": "The impact of an anti-unitary symmetry on the spectrum of non-hermitean\noperators is studied. Wigner\u0027s normal form of an anti-unitary operator is shown\nto account for the spectral properties of non-hermitean, PT-symmetric\nHamiltonians. Both the occurrence of single real or complex conjugate pairs of\neigenvalues follows from this theory. The corresponding energy eigenstates span\neither one- or two-dimensional irreducible representations of the symmetry PT.\nIn this framework, the concept of a spontaneously broken PT-symmetry is not\nneeded.",
"arxiv_id": "quant-ph/0209054",
"authors": [
"Stefan Weigert"
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"doi": "10.1088/1464-4266/5/3/380",
"journal_ref": "J. Opt. B 5 (2003) S416",
"title": "PT-symmetry and its spontaneous breakdown explained by anti-linearity",
"url": "https://arxiv.org/abs/quant-ph/0209054"
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