|
| related topics |
| {operator, operators, space} |
| {group, space, representation} |
| {energy, state, states} |
| {cos, sin, state} |
| {equation, function, exp} |
| {force, casimir, field} |
|
PT-symmetry and its spontaneous breakdown explained by anti-linearity
Stefan Weigert
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0209054
- categories:
- quant-ph
- comments:
- 8 pages
- doi:
- 10.1088/1464-4266/5/3/380
- arxiv_id:
- quant-ph/0209054
- journal_ref:
- J. Opt. B 5 (2003) S416
- created:
- 2002-09-06
Full article ▸
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