Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-10-04
J.Math.Phys. 39 (1998) 3437-3452
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 26 pages, no figures. Extended changes. Final Version to appear in J. Math. Phys
Scientific paper
10.1063/1.532439
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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