×

Coherent state quantization of paragrassmann algebras. (English) Zbl 1198.81124

J. Phys. A, Math. Theor. 43, No. 38, Article ID 385202, 15 p. (2010); corrigendum ibid. 45, No. 7, Article ID 079501, 2 p. (2012).
Summary: By using a coherent state quantization of para-Grassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the para-Grassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

MSC:

81R30 Coherent states
81S05 Commutation relations and statistics as related to quantum mechanics (general)
81R15 Operator algebra methods applied to problems in quantum theory
15A75 Exterior algebra, Grassmann algebras
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Gazeau J-P 2009 Coherent States in Quantum Physics (Berlin: Wiley-VCH) · doi:10.1002/9783527628285
[2] Filippov A T, Isaev A P and Kurdikov A B 1992 Mod. Phys. Lett. A 7 2129 · Zbl 1021.81570 · doi:10.1142/S0217732392001877
[3] Isaev A P 1997 Paragrassmann integral, discrete systems and quantum groups Int. J. Mod. Phys. A 12 201 (arXiv:q-alg/9609030) · Zbl 1073.81613 · doi:10.1142/S0217751X97000281
[4] Rausch de Traubenberg M 1997 Algèbres de Clifford Supersymétrie et Symétrie Zn Applications en Théorie des Champs Habilitation à diriger des recherches Université Louis Pasteur (Unpublished)
[5] Rubakov V A and Spiridonov V P 1988 Mod. Phys. Lett. A 3 1337 · doi:10.1142/S0217732388001616
[6] Durand S, Floreanini R, Mayrand M and Vinet L 1989 Phys. Lett. B 233 158 · doi:10.1016/0370-2693(89)90633-3
[7] Spiridonov V P 1990 Proc. Int. Seminar Quarks-90(Telavi, USSR, May 1990) ed V A Matveev et al (Singapore: World Scientific)
[8] de Azcarraga J A and Macfarlane A J 1996 J. Math. Phys.37 1115 · Zbl 0865.58052 · doi:10.1063/1.531451
[9] Durand S 1993 Phys. Lett. B 312 115 · doi:10.1016/0370-2693(93)90496-5
[10] Govorkov A B 1983 Sov. J. Part. Nucl.14 520
[11] Ohnuki Y and Kamefuchi S 1982 Quantum Field Theory and Parastatistics (Tokyo: University of Tokyo Press) 489p · Zbl 0566.46041 · doi:10.1007/978-3-642-68622-1
[12] Ahn C, Bernard D and LeClair A 1990 Nucl. Phys. B 346 409 · doi:10.1016/0550-3213(90)90287-N
[13] Greenberg O 1991 Phys. Rev. D 43 4111 · doi:10.1103/PhysRevD.43.4111
[14] Forte S 1992 Rev. Mod. Phys.64 193 · doi:10.1103/RevModPhys.64.193
[15] Majid S and Rodriguez-Plaza M 1994 J. Math. Phys.35 3753 · Zbl 0808.60090 · doi:10.1063/1.530868
[16] Berezin F A 1975 Commun. Math. Phys.40 153 · Zbl 1272.53082 · doi:10.1007/BF01609397
[17] Klauder J R and Skagerstam B S 1985 Coherent States, Applications in Physics and Mathematical Physics (Singapore: World Scientific) p 991 · Zbl 1050.81558 · doi:10.1142/0096
[18] Lieb E H 1973 Commun. Math. Phys.31 327 · Zbl 1125.82305 · doi:10.1007/BF01646493
[19] Berezin F A 1965 The Method of Second Quantization (Moscow: Nauka) · Zbl 0131.44805
[20] Daoud B M, Hassouni Y and Kibler M 1998 Generalized supercoherent states Phys. Atom. Nuclei.61 1821-4
[21] Daoud B M, Hassouni Y and Kibler M 1998 Yad. Fiz.61 1935-8
[22] Daoud M and Kibler M 2002 A fractional supersymmetric oscillator and its coherent states ed M Arik et alProc. Int. Wigner Symp.(Istanbul, August 1999) (Istanbul: Bogazici University Press)
[23] El Baz M, Hassouni Y and Madouri F 2002 Phys. Lett. B 536 321 · Zbl 0995.81028 · doi:10.1016/S0370-2693(02)01834-8
[24] El Baz M and Hassouni Y 2004 J. Phys. A: Math. Gen.35 4361 · Zbl 1052.81047 · doi:10.1088/0305-4470/37/15/005
[25] Chaichian M and Demichev A 1996 Introduction to Quantum Groups (Singapore: World Scientific) · Zbl 0930.17009 · doi:10.1142/9789814261067
[26] Ghanmi A 2008 J. Math. Anal.340 1395 · Zbl 1229.33017 · doi:10.1016/j.jmaa.2007.10.001
[27] Intissar A and Intissar A 2006 J. Math. Anal. Appl.313 400 · Zbl 1100.47029 · doi:10.1016/j.jmaa.2005.09.056
[28] Biedenharn L C 1989 J. Phys. A: Math. Gen.22 L873 · Zbl 0708.17015 · doi:10.1088/0305-4470/22/18/004
[29] Macfarlane A J 1989 J. Phys. A: Math. Gen.22 4581-8 · Zbl 0722.17009 · doi:10.1088/0305-4470/22/21/020
[30] Andrews G E and Onofri E 1984 Special Functions: Group Theoretical Aspects and Applications ed R A Askey, T H Koornwinder and W Schempp (Dordrecht: Reidel) p 163 · Zbl 0543.00007
[31] Chakraborty B, Gazeau J-P and Youssef A 2008 Coherent state quantization of angle, time, and more irregular functions and distributions arXiv:0805.1847v1
[32] Daoud M, Hassouni Y and Kibler M 1998 Symmetries in Science: X ed B Gruber and M Ramek (New York: Plenum)
[33] Berezin F and Marinov M 1977 Ann. Phys.104 336 · Zbl 0354.70003 · doi:10.1016/0003-4916(77)90335-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.