Deforming Maps for Lie Group Covariant Creation and Annihilation Operators

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.

Latex file, 26 pages, no figures. Extended changes. Final Version to appear in J. Math. Phys

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