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SIGMA 2 (2006), 087, 8 pages hep-th/0609217
https://doi.org/10.3842/SIGMA.2006.087
Contribution to the Proceedings of the O'Raifeartaigh Symposium
Para-Grassmann Variables and Coherent States
Daniel C. Cabra a, b, c, Enrique F. Moreno c, d and Adrian Tanasă e
a) Laboratoire de Physique Théorique, CNRS UMR 7085, Université L. Pasteur,
3 rue de l'Université, F-67084 Strasbourg Cedex, France
b) Facultad de Inginería, Universidad Nacional de lomas de Zamora,
Cno. de Cintura y Juan XXIII, (1832) Lomas de Zamora, Argentina
c) Departamento de Física, Facultad de
Ciencias Exactas, Universidad Nacional de La Plata, C. C. 67, 1900 La Plata, Argentina
d) Department of Physics, West Virginia University,
Morgantown, West Virginia 26506-6315, USA
e) Laboratoire de Physique Théorique, Bât.
210, CNRS UMR 8627, Université Paris XI, F-91405 Orsay Cedex, France
Received September 29, 2006, in final form November 22, 2006; Published online December 07, 2006
Abstract
The definitions of para-Grassmann variables and
q-oscillator algebras are recalled. Some new properties are
given. We then introduce appropriate coherent states as well as
their dual states. This allows us to obtain a formula for the
trace of a operator expressed as a function of the creation and
annihilation operators.
Key words:
para-Grassmann variables; q-oscillator algebra; coherent states.
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References
- Ohnuki Y., Kamefuchi S., Quantum field theory and
parastatistics, New York, Springer-Verlag, 1982.
- Polychronakos A.P., A classical realization of quantum algebras,
Modern Phys. Lett. A, 1990, V.5, 2325-2334.
- Baulieu L., Floratos E.G., Path integral on the quantum plane,
Phys. Lett. B, 1991, V.258, 171-178.
- Filippov A.T., Isaev A.P., Kurdikov A.B., ParaGrassmann analysis
and quantum groups, Modern Phys. Lett. A, 1992, V.7,
2129-2142, gr-qc/9204089.
- Filippov A.T., Isaev A.P. , Kurdikov A.B., ParaGrassmann
differential calculus, Theor. Math. Phys., 1993, V.94,
150-165, hep-th/9210075.
- Chaichian M., Demichev A.P., q-deformed path integral,
Phys. Lett. B, 1994, V.320, 273-280,
hep-th/9310001.
- Isaev A.P., Paragrassmann integral, discrete systems and quantum
groups, Internat. J. Modern Phys. A, 1997, V.12,
201-206, q-alg/9609030.
- Chaichian M., Demichev A.P., Path integrals with generalized
Grassmann variables,
q-alg/9504016.
- Ilinski K.N., Kalinin G.V., Stepanenko A.S., q-functional
field theory for particles with exotic statistics, Phys. Lett. A, 1997, V.232, 399-408,
hep-th/9705086.
- Ilinski K.N., Kalinin G.V., Stepanenko A.S., q-functional Wick's
theorems for particles with exotic statistics, J. Phys. A:
Math. Gen., 1997, V.30, 5299-5310,
hep-th/9704181.
- Rausch de Traubenberg M., Clifford algebras, supersymmetry and
Z(n) symmetries: applications in field theory,
hep-th/9802141 (in
French).
- Daoud M., Hassouni Y., Kibler M., Generalized supercoherent
states, Phys. Atomic Nuclei, 1998, V.61, 1821-1864,
quant-ph/9804046.
- Daoud M., Kibler M., A fractional supersymmetric oscillator and
its coherent states,
math-ph/9912024.
- Cugliandolo L.F., Lozano G.S., Moreno E.F., Schaposnik F.A., A
note on Gaussian integrals over paragrassmann variables,
Internat. J. Modern Phys. A, 2004, V.19, 1705-1714,
hep-th/0209172.
- Biedenharn L.C., The quatum group SU(2)-q and a q analog of
the boson operators, J. Phys. A: Math. Gen., 1989, V.22,
873-878.
- Macfarlane A.J., On q analogs of the quantum harmonic oscillator
and the quatum group SU(2)-q, J. Phys. A: Math. Gen.,
1989, V.22, 4581-4588.
- Karabali D., Nair V.P., Many body states and operator algebra for
exclusion statistics, Nuclear Phys. B, 1995, V.438,
551-560.
- Negele J.W., Orland H., Quantum many-particle systems, Cambridge,
Perseus, 1988.
- Cabra D., Moreno E., Tanasă A., Para-Grassmann variables and coherent states for multi-particle
states, in progress.
- Rausch de Traubenberg M., Fleury N., Beyond spinors, in Leite Lopes
Festschrift, Editors N. Fleury et al., Singapore, World Scientific, 1988, 79-101.
- Hayashi T., Q-analogues of Clifford and Weyl algebras - spinor
and oscillator reoresentations of quantum enveloping algebras,
Comm. Math. Phys., 1990, V.127, 129-144.
- Chaichian M., Kulish P., Quantum Lie superalgebras and q
oscillators, Phys. Lett. B, 1990, V.234, 72-80.
- Fivel D., Interpolation between Fermi and Bose statistics using
generalized commutators, Phys. Rev. Lett., 1990, V.65, 3361-3364.
- Greenberg O.W., Quon statistics, Phys. Rev. D, 1991,
V.43, 4111-4120.
- Klauder J.R., Skagerstam B., Coherent states: applications in
physics and mathematical physics, World Scientific, 1985.
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