q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors
We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.
Unable to display preview. Download preview PDF.
- Proceedings of the 8th Int. Workshop on Mathematical Physics (Quantum Groups), Clausthal 1989, H.-D. Doebner and J.-D. Jenning (Eds.), Lect. Notes in Physics 370, Springer Verlag (1990).Google Scholar
- Proceedings of the First Euler Math. Inst. Workshop on quantum groups (1990), P. Kulish Ed., Springer-Verlag, (1991).Google Scholar
- Yu. I. Manin, Quantum groups and non-commutative geometry, Centre des Recherches Mathématiques, Montréal (1988).Google Scholar
- O. Ogievetsky, W.B. Schmidke, J. Wess and B. Zumino, Six generator q-deformed Lorentz algebra, MPI-Ph/91-51,(1991); q-deformed Poincaré algebra, MPI-Ph/ 91-98, (1991).Google Scholar
- V. K. Dobrev, Canonical q-deformations of Non-compact Lie (Super-) Algebras, Göttingen preprint (July/October 1991); q-deformations of non-compact Lie (Super-) Algebras: the examples of q-deformed Lorentz, Weyl, Poincaré and (Super-) conformal algebra, ICTP preprint IC/92/13, to appear in the Proc. of the II Wigner Symposium, Goslar (1991).Google Scholar
- O. Ogievetsky, M. Pillin, W.B. Schmidke, J. Wess and B. Zumino, q-Deformed Minkowski space, in the Proc. of the XIX Int. Colloquium on Group Theoretical Methods in Physics, Salamanca July 1992, J. Mateos, M. del Olmo and M. Santander (Eds.), to be published by CIEMAT-Real Soc. Española de Física.Google Scholar
- J. Schwinger, On angular momentum, Report U.S. AEC NYO-3071 (unpublished). Reprinted in Quantum theory of angular momentum L.C. Biedenharn Ed., Acad. Press p. 229 (1965).Google Scholar
- L. C. Biedenharn, A q-boson realization of the quantum group su(2) q and the theory of q-tensor operators, in Proc. of the Clausthal Summer Workshop on Math. Physics, H.-D. Doebner and J.-D. Jenning Eds., Springer-Verlag (1991).Google Scholar
- L. C. Biedenharn and M. A. Lohe, Induced representations and tensor operators for quantum groups, in the First Euler Math. Workshop on Quantum Groups, P. Kulish Ed., Springer Verlag (1991).Google Scholar
- C. Quesne, q-bosons and irreducible tensors for q-algebras, Bruxelles PNT /10/92 preprint (1992) and these Proceedings.Google Scholar