Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.
Sektion Physik, Universität München, LS Prof. Wess, Theresienstr. 37, D-80333 München, Germany
Bibliografia
[1] W. Pusz, S. L. Woronowicz, Twisted Second Quantization, Reports on Mathematical Physics 27 (1989), 231-257.
[2] G. Fiore, P. Schupp, Identical Particles and Quantum Symmetries, Preprint LMU-TPW 95-10 (Munich University), hep-th 9508047, to appear in Nucl. Phys. B.
[3] V. G. Drinfeld, Quasi Hopf Algebras, Leningrad Math. J. 1 (1990), 1419.
[4] V. G. Drinfeld, Doklady AN SSSR 273 (1983) (in Russian), 531-535.
[5] B. Jurco, More on Quantum Groups from the Quantization Point of View, Commun. Math. Phys. 166 (1994), 63.
[6] O. Ogievetsky, W. B. Schmidke, J. Wess and B. Zumino, q-Deformed Poincaré Algebra, Commun. Math. Phys. 150 (1992) 495-518.
[7] S. Majid, Braided Momentum in the q-Poincaré Group, J. Math. Phys. 34 (1993), 2045.
[8] M. Pillin, W. B. Schmidke and J. Wess, q-Deformed Relativistic One-Particle States, Nucl. Phys. B403 (1993), 223.
[9] G. Fiore, The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations, J. Math. Phys. 36 (1995), 4363-4405; The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice, Int. J. Mod. Phys. A, in press.
[10] F. Bonechi, R. Giachetti, E. Sorace, M. Tarlini, Deformation Quantization of the Heisenberg Group, Commun. Math. Phys. 169 (1995), 627-633.
[11] R. Engeldinger, On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups, Preprint LMU-TPW 95-13.
[12] T. L. Curtright, G. I. Ghandour, C. K. Zachos, Quantum Algebra Deforming Maps, Clebsh-Gordan Coefficients, Coproducts, U and R Matrices, J. Math. Phys. 32 (1991), 676-688.