Deforming Maps for Lie Group Covariant Creation & Annihilation Operators

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 Uhg 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 Uhg . The method is then generalized and explicitly applied to the case that Uhg is the quantum group Uhsl(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 Uhg can be interpreted as standard ‘undeformed’ Fock representations describing particles with ordinary Bose or Fermi statistics. PACS: 02.20.-a, 03.65.Fd, 05.30.-d, 11.30.-j *EU-fellow, TMR grant ERBFMBICT960921. e-mail: Gaetano.Fiore @ physik.uni-muenchen.de