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.
Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras / Fiore, Gaetano. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - STAMPA. - 12:(2000), pp. 327-359.
Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
FIORE, GAETANO
2000
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.