Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras

Abstract

Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are characterized by their being covariant under the action of the quantum group $U_{q}g$. We present a systematic procedure for determining all possible corresponding changes of generators, together with the corresponding realizations of the $U_{q}g$-action. The intriguing relation between g-invariants and $U_{q}g$-invariants suggests that these changes of generators might be employed to simplify the dynamics of some g-covariant quantum physical systems.

latex file, 35 pages, no figures. Final version to appear in Rev. Math. Phys

References in corpus (1)

• Deforming Maps for Lie Group Covariant Creation and Annihilation Operators

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