dorsal/arxiv
View SchemaNoncanonical quantum optics
| Authors | Marek Czachor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0003091 |
| URL | https://arxiv.org/abs/quant-ph/0003091 |
| DOI | 10.1088/0305-4470/33/45/307 |
| Journal | J.Phys.A33:8081-8104,2000 |
Abstract
Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of electromagnetic field by means of such a non-CCR algebra naturally removes the infinite energy of vacuum but still results in a theory which is very similar to quantum electrodynamics. An analysis of perturbation theory shows that the non-canonical theory has an automatically built-in cut-off but requires charge/mass renormalization already at the nonrelativistic level. A simple rule allowing to compare perturbative predictions of canonical and non-canonical theories is given. The notion of a unique vacuum state is replaced by a set of different vacua. Multi-photon states are defined in the standard way but depend on the choice of vacuum. Making a simplified choice of the vacuum state we estimate corrections to atomic lifetimes, probabilities of multiphoton spontaneous and stimulated emission, and the Planck law. The results are practically identical to the standard ones. Two different candidates for a free-field Hamiltonian are compared.
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"abstract": "Modification of the right-hand-side of canonical commutation relations (CCR)\nnaturally occurs if one considers a harmonic oscillator with indefinite\nfrequency. Quantization of electromagnetic field by means of such a non-CCR\nalgebra naturally removes the infinite energy of vacuum but still results in a\ntheory which is very similar to quantum electrodynamics. An analysis of\nperturbation theory shows that the non-canonical theory has an automatically\nbuilt-in cut-off but requires charge/mass renormalization already at the\nnonrelativistic level. A simple rule allowing to compare perturbative\npredictions of canonical and non-canonical theories is given. The notion of a\nunique vacuum state is replaced by a set of different vacua. Multi-photon\nstates are defined in the standard way but depend on the choice of vacuum.\nMaking a simplified choice of the vacuum state we estimate corrections to\natomic lifetimes, probabilities of multiphoton spontaneous and stimulated\nemission, and the Planck law. The results are practically identical to the\nstandard ones. Two different candidates for a free-field Hamiltonian are\ncompared.",
"arxiv_id": "quant-ph/0003091",
"authors": [
"Marek Czachor"
],
"categories": [
"quant-ph",
"hep-th",
"physics.atom-ph"
],
"doi": "10.1088/0305-4470/33/45/307",
"journal_ref": "J.Phys.A33:8081-8104,2000",
"title": "Noncanonical quantum optics",
"url": "https://arxiv.org/abs/quant-ph/0003091"
},
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