dorsal/arxiv
View SchemaNon-canonical quantum optics (II): Poincar\'e covariant formalism and thermodynamic limit
| Authors | Marek Czachor, Monika Syty |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205011 |
| URL | https://arxiv.org/abs/quant-ph/0205011 |
Abstract
The paper contains further development of the idea of field quantization introduced in M. Czachor, J. Phys. A: Math. Gen. {\bf 33} (2000) 8081-8103. The formalism is extended to the relativistic domain. The link to the standard theory is obtained via a thermodynamic limit. Unitary representations of the Poincar\'e group at the level of fields and states are explicitly given. Non-canonical multi-photon and coherent states are introduced. In the thermodynamic limit the statistics of photons in a coherent state is Poissonian. The $S$ matrix of radiation fields produced by a classical current is given by a non-canonical coherent-state displacement operator, a fact automatically eliminating the infrared catastrophe. Field operators are shown to be operators and not operator-valued distributions, and can be multiplied at the same point in configuration space. An exactly solvable example is used to compare predictions of the standard theory with those of non-canonical quantum optics, and explicitly shows the mechanism of automatic ultraviolet regularization occuring in the non-canonical theory. Similar conclusions are obtained in perturbation theory, where one finds the standard Feynman diagrams, but the Feynman rules are modified. A comparison with the Dicke-Hepp-Lieb model allows to identify the physical structure behind the non-canonical algebra as corresponding to an ensemble of indefinite-frequency oscillators with constant density $N/V$.
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"abstract": "The paper contains further development of the idea of field quantization\nintroduced in M. Czachor, J. Phys. A: Math. Gen. {\\bf 33} (2000) 8081-8103. The\nformalism is extended to the relativistic domain. The link to the standard\ntheory is obtained via a thermodynamic limit. Unitary representations of the\nPoincar\\\u0027e group at the level of fields and states are explicitly given.\nNon-canonical multi-photon and coherent states are introduced. In the\nthermodynamic limit the statistics of photons in a coherent state is\nPoissonian. The $S$ matrix of radiation fields produced by a classical current\nis given by a non-canonical coherent-state displacement operator, a fact\nautomatically eliminating the infrared catastrophe. Field operators are shown\nto be operators and not operator-valued distributions, and can be multiplied at\nthe same point in configuration space. An exactly solvable example is used to\ncompare predictions of the standard theory with those of non-canonical quantum\noptics, and explicitly shows the mechanism of automatic ultraviolet\nregularization occuring in the non-canonical theory. Similar conclusions are\nobtained in perturbation theory, where one finds the standard Feynman diagrams,\nbut the Feynman rules are modified. A comparison with the Dicke-Hepp-Lieb model\nallows to identify the physical structure behind the non-canonical algebra as\ncorresponding to an ensemble of indefinite-frequency oscillators with constant\ndensity $N/V$.",
"arxiv_id": "quant-ph/0205011",
"authors": [
"Marek Czachor",
"Monika Syty"
],
"categories": [
"quant-ph",
"hep-th",
"physics.atom-ph"
],
"title": "Non-canonical quantum optics (II): Poincar\\\u0027e covariant formalism and thermodynamic limit",
"url": "https://arxiv.org/abs/quant-ph/0205011"
},
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