Abstract
Deformed commutation relations and corresponding consistency conditions with braid relations are studied in terms of the so-called Wick algebras. We discuss the construction of such algebras and give some examples.
This work is partially supported by KBN, Grant No 2P 302 087 06
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Pusz, Rep. Math. Phys. 27: 394 (1989)
W. Pusz and S.L. Woronowicz, Rep. Math. Phys 27: 231, (1989)
D.B. Fairlie and C.K. Zachos, Phys. Lett. B 256: 43 (1991)
S.P. Vokos, J. Math. Phys. 32: 2979 (1991)
M. Arik, The q-difference operator, the ‘quantum hyperplane, Hilbert spaces of analytic funtions and q-oscillators, Istanbul Technical University preprint (1991)
S. Majid, Free braided differential calculus, braided binomial theorem and the braided exponential map, preprint DAMTP/93-3 (1993)
A. Kempf, Lett. Math. Phys. 26: 11 (1992)
M. Bożejko, R. Speicher, Interpolation between bosonic and fermionic relations given by generalized Brownian motions, preprint FSB 132-691, Heidelberg (1992)
M. Bożejko, R. Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces (in preparation)
P.E.T. Jørgensen, L.M. Schmith, and R.F. Werner, Positive representation of general commutation relations allowing Wick ordering, preprint (1993)
J. C. Baez, R-commutative geometry and quantization of Poisson algebras, Wellesley College preprint (July 1991)
A. Borowiec, V. K. Kharchenko, Z. Oziewicz, Calculi on Clifford-Weyl and exterior algebras for Hecke braiding, Conferencia dictata por Zbigniew Oziewicz at Centro de Investigation en Matematicas, Guanajuato, Mexico, Seminario de Geometria, jueves 22 de abril de 1993 and at the Conference on Differential Geometric Methods, Ixtapa, Mexico, September 1993
E. E. Demidov, On some aspects of the theory of quantum groups, Uspekhi Mat. Nauk 48(6): 39 (1993) (Russian)
J. Wess and B. Zumino, Covariant differential calculus on the quantum hyperplane, CERN preprint 5697/90 (1990)
W. Marcinek, On braid statistics and noncommutative calculus, Rep. Math. Phys. 33: 117 (1993)
W. Marcinek, On unital braidings and quantization, U. Wrocław preprint ITP-847 (1993)
W. Marcinek, Noncommutative geometry corresponding to arbitrary braidings, J. Math. Phys. 35: 2633 (1994)
W. Marcinek and R. Rałowski, Particle operators from braided geometry, Proceedings of the XXX Winter School of Theoretical Physics, Karpacz, Poland, February 15-26 (1994)
C. Daskaloyannis, J. Phys. A 24: L789 (1991)
D. I. Fivel, Phys. Rev. Lett. 65: 3361 (1990)
J. C. Baez, Lett Math. Phys. 23: 1333 (1991)
V.V. Lyubashenko, Vectorsymmetries, Seminar on Supermanifolds No 19: 1 (1987)
D. Gurevich, A. Radul and V. Rubstov, Noncommutative differential geometry and Yang-Baxter equation, I.H.E.S./M/91/88 (1988)
Y. I. Manin, Quantum groups and noncommutative geometry, University of Montreal preprint (1989)
W. Marcinek, Algebras based on Yang-Baxter operators, Rep. Math. Phys. 32: 1 (1993)
W. Marcinek, On colour quantization: relations and parastatistics, Mod. Phys. Lett. (1995) (to appear).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Marcinek, W. (1995). On The Deformation of Commutation Relations. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization, Coherent States, and Complex Structures. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1060-8_23
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1060-8_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1062-2
Online ISBN: 978-1-4899-1060-8
eBook Packages: Springer Book Archive