Abstract
A representation theory of the quantized Poincaré (κ-Poincaré) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the nondeformed Poincaré algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed. These results are used for the construction of someq-relativistic equations. The Wigner-Eckart theorem for QPA is proven.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Celeghini, E. Giachetti, R., Sorace, E., and Tarlini, M.,J. Math. Phys. 31, 2548–2551 (1990);32, 1155-1158 (1991);32, 1159-1165 (1991) and Contractions of quantum groups, inQuantum Groups, Lecture Notes in Mathematics 1510 Springer-Verlag, New York, 1992, p. 221.
Lukierski, J., Nowicki, A., Ruegg, H., and Tolstoy, V. N.,Phys. Lett. B 264, 331–338 (1991).
Giller, S., Kunz, Y., Kosinski, P., Majewski, M., and Maslanka, P.,Phys. Lett. B 286, 57–61 (1992).
Lukierski, J., Nowicki, A., and Ruegg, H.,Phys. Lett. B 293, 344–352 (1992).
Lukierski, J. and Ruegg, H., Quantumκ-Poincaré in any dimension,Phys. Lett. B 329, 189–194 (1994).
Domokos, G. and Kovesi-Domokos, S., Astrophysical limit on the deformation of the Poincaré group, Preprint JHK-TIPAC-920027/REV (1993).
Lukierski, J., Ruegg, H., and Rühl, W.,Phys. Lett. B 313, 357–366 (1993).
Biedenharn, L. C., Mueller, B., and Tarlini, M., The Dirac-Coulomb problems for theκ-Poincaré quantum group,Phys. Lett. B 318, 613–616 (1993).
Ruegg, H.,q-Deformation of semisimple and non-semisimple Lie algebras in L. A. Ibort and M. A. Rodriguez (eds),Integrable Systems, Quantum Groups and Quantum Field Theories, Kluwer Academic Publishers, Dordrecht, 1993, pp. 45–81.
Giller, S., Gonera, C., Kosinski, P., Majewski, M., Maslanka, P., and Kunz, J. Onq-covariant wave functions,Modern Phys. Lett. A 40 3785–3797 (1993).
Maslanka, P., Deformation map and Hermitean representations ofκ-Poincaré algebra,J. Math. Phys. 34, 6025–6029 (1993); Global counterpart ofκ-Poincaré algebra and covariant wave functions, Preprint 5/93, IM UL.
Tolstoy, V. N., Tensor operators for quantized Kac-Moody (super) algebras, in preparation.
Tolstoy, V. N., Extremal projectors for quantized Kac-Moody (super) algebras and some of their applications.Proc. Quantum Groups Workshop, Clausthal, Germany (July 1989). Lecture Notes in Physics 370, Springer-Verlag, New York, 1990, pp. 118–125.
Biedenharn, L. C. and Tarlini, M.,Lett. Math. Phys. 20, 271–278 (1990).
Smirnov, Yu. F., Tolstoy, V. N., and Kharitonov, Yu. I.,J. Nuclear Phys. 53 (4), 959–980 (1991);53 (6), 1746-1771 (1991);55 (10), 2863-2874 (1992);56 (5), 236-257 (1993) (in Russian).
Rittenberg, V. and Scheunert, M.,J. Math. Phys. 33, 436–445 (1992).
Bacry, H.,Phys. Lett. B 306, 41–43 (1993).
Nowicki, A., Sorace, E., and Tarlini, M.,Phys. Lett. B 302, 419–422 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ruegg, H., Tolstoy, V.N. Representation theory of quantized poincaré algebra. tensor operators and their applications to one-particle systems. Lett Math Phys 32, 85–101 (1994). https://doi.org/10.1007/BF00739419
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00739419