Statistics and quantum group symmetries

Gaetano Fiore; Peter Schupp

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 369-377
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Fiore, Gaetano, and Schupp, Peter. "Statistics and quantum group symmetries." Banach Center Publications 40.1 (1997): 369-377. <http://eudml.org/doc/252192>.

@article{Fiore1997,
abstract = {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.},
author = {Fiore, Gaetano, Schupp, Peter},
journal = {Banach Center Publications},
keywords = {twisted transformations; Hopf algebra; quantum group transformations; quantum mechanics; Bose and Fermi statistics; compact quantum groups},
language = {eng},
number = {1},
pages = {369-377},
title = {Statistics and quantum group symmetries},
url = {http://eudml.org/doc/252192},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Fiore, Gaetano
AU - Schupp, Peter
TI - Statistics and quantum group symmetries
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 369
EP - 377
AB - 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.
LA - eng
KW - twisted transformations; Hopf algebra; quantum group transformations; quantum mechanics; Bose and Fermi statistics; compact quantum groups
UR - http://eudml.org/doc/252192
ER -

References

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  1. [1] W. Pusz, S. L. Woronowicz, Twisted Second Quantization, Reports on Mathematical Physics 27 (1989), 231-257. Zbl0707.47039
  2. [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. Zbl1003.81504
  3. [3] V. G. Drinfeld, Quasi Hopf Algebras, Leningrad Math. J. 1 (1990), 1419. 
  4. [4] V. G. Drinfeld, Doklady AN SSSR 273 (1983) (in Russian), 531-535. 
  5. [5] B. Jurco, More on Quantum Groups from the Quantization Point of View, Commun. Math. Phys. 166 (1994), 63. Zbl0824.17013
  6. [6] O. Ogievetsky, W. B. Schmidke, J. Wess and B. Zumino, q-Deformed Poincaré Algebra, Commun. Math. Phys. 150 (1992) 495-518. 
  7. [7] S. Majid, Braided Momentum in the q-Poincaré Group, J. Math. Phys. 34 (1993), 2045. Zbl0786.17013
  8. [8] M. Pillin, W. B. Schmidke and J. Wess, q-Deformed Relativistic One-Particle States, Nucl. Phys. B403 (1993), 223. 
  9. [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. [10] F. Bonechi, R. Giachetti, E. Sorace, M. Tarlini, Deformation Quantization of the Heisenberg Group, Commun. Math. Phys. 169 (1995), 627-633. Zbl0833.17017
  11. [11] R. Engeldinger, On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups, Preprint LMU-TPW 95-13. 
  12. [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. Zbl0749.17011

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