dorsal/arxiv
View SchemaDeforming Maps for Lie Group Covariant Creation and Annihilation Operators
| Authors | Gaetano Fiore |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9610005 |
| URL | https://arxiv.org/abs/q-alg/9610005 |
| DOI | 10.1063/1.532439 |
| Journal | J.Math.Phys. 39 (1998) 3437-3452 |
Abstract
Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some triangular deformation $U_h g$ of the Hopf algebra $Ug$. We propose a systematic method to construct all the corresponding deforming maps, together with the corresponding realizations of the action of $U_h g$. The method is then generalized and explicitly applied to the case that $U_h g$ is the quantum group $U_h sl(2)$. A preliminary study of the status of deforming maps at the representation level shows in particular that `deformed' Fock representations induced by a compact $U_h g$ can be interpreted as standard `undeformed' Fock representations describing particles with ordinary Bose or Fermi statistics.
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"abstract": "Any deformation of a Weyl or Clifford algebra A can be realized through a\n`deforming map\u0027, i.e. a formal change of generators in A. This is true in\nparticular if A is covariant under a Lie algebra g and its deformation is\ninduced by some triangular deformation $U_h g$ of the Hopf algebra $Ug$. We\npropose a systematic method to construct all the corresponding deforming maps,\ntogether with the corresponding realizations of the action of $U_h g$. The\nmethod is then generalized and explicitly applied to the case that $U_h g$ is\nthe quantum group $U_h sl(2)$. A preliminary study of the status of deforming\nmaps at the representation level shows in particular that `deformed\u0027 Fock\nrepresentations induced by a compact $U_h g$ can be interpreted as standard\n`undeformed\u0027 Fock representations describing particles with ordinary Bose or\nFermi statistics.",
"arxiv_id": "q-alg/9610005",
"authors": [
"Gaetano Fiore"
],
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"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1063/1.532439",
"journal_ref": "J.Math.Phys. 39 (1998) 3437-3452",
"title": "Deforming Maps for Lie Group Covariant Creation and Annihilation Operators",
"url": "https://arxiv.org/abs/q-alg/9610005"
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