Deforming maps for Lie group covariant creation and 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 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. (C) 1998 American Institute of Physics.