Generalized coherent states: a novel approach
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 65-71 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We define generalized coherent states for oscillator-like systems connected with orthogonal polynomials (classical, $q$-deformed etc.). In considered cases such polynomials play the same role, as the Hermite polynomials are defined in the case of usual boson oscillator.
@article{ZNSL_2003_300_a6,
     author = {V. V. Borzov and E. V. Damaskinsky},
     title = {Generalized coherent states: a~novel approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {65--71},
     year = {2003},
     volume = {300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a6/}
}
TY  - JOUR
AU  - V. V. Borzov
AU  - E. V. Damaskinsky
TI  - Generalized coherent states: a novel approach
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 65
EP  - 71
VL  - 300
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a6/
LA  - en
ID  - ZNSL_2003_300_a6
ER  - 
%0 Journal Article
%A V. V. Borzov
%A E. V. Damaskinsky
%T Generalized coherent states: a novel approach
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 65-71
%V 300
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a6/
%G en
%F ZNSL_2003_300_a6
V. V. Borzov; E. V. Damaskinsky. Generalized coherent states: a novel approach. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems. Part VIII, Tome 300 (2003), pp. 65-71. http://geodesic.mathdoc.fr/item/ZNSL_2003_300_a6/

[1] J. R. Klauder, B.-S. Skagerstam (eds.), Coherent States: Applications in Physics and Mathematical Physics, World Scientific, Singapore, 1985 | MR | Zbl

[2] Kogerentnye sostoyaniya v kvantovoi teorii. Novosti fundamentalnoi fiziki, vyp. 1, Mir, Moskva, 1972 | MR

[3] A. I. Baz, Ya. B. Zeldovich, A. M. Perelomov, Rasseyanie, reaktsii i raspady v nerelyativistskoi kvantovoi mekhanike, 2-e izd., Nauka, Moskva, 1971 | Zbl

[4] Dzh. Klauder, E. Sudarshan, Osnovy kvantovoi optiki, Mir, Moskva, 1970 | Zbl

[5] P. P. Kulish, L. D. Faddeev, “Asimptoticheskie usloviya i infrakrasnye raskhodimosti”, Teor. matem. fiz., 4:2 (1970), 153–170

[6] V. N. Popov, Kontinualnye integraly v kvantovoi teorii polya i statisticheskoi fizike, “Atomizdat”, Moskva, 1980 | MR

[7] V. N. Popov, V. S. Yarunin, Kogerentnye kollektivnye yavleniya v sverkhprovodimosti i nelineinoi optike, SPbGU, S.-Peterburg, 1994

[8] A. M. Perelomov, Obobschennye kogerentnye sostoyaniya i ikh primeneniya, Nauka, Moskva, 1987 | MR

[9] E. Schrödinger, “Der stetige Übergang von der Mikro- zur Macromechanik”, Naturwissenshaften, 14 (1926), 644–666 | DOI

[10] R. J. Glauber, “The Quantum Theory of Optical Coherence”, Phys. Rev., 130 (1963), 2529–2539 | DOI | MR

[11] R. J. Glauber, “Coherent and incoherent states of radiation field”, Phys. Rev., 131 (1963), 2766–2788 | DOI | MR

[12] J. R. Klauder, “The action option and a Feynman quantization of spinor fields in terms of ordinary $c$-numbers”, Ann. Phys., 11 (1960), 123–168 | DOI | MR | Zbl

[13] E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams”, Phys. Rev. Lett., 10 (1963), 277–279 | DOI | MR | Zbl

[14] V. Bargmann, “On a Hilbert space of analytic functions and associated integral transform, I”, Comm. Pure Appl. Math., 14 (1961), 187–214 | DOI | MR | Zbl

[15] V. Bargmann, “On a Hilbert space of analytic functions and associated integral transform. 2: A family of related function spaces. Application to distribution theory”, Comm. Pure Appl. Math., 20 (1967), 1–101 | DOI | MR | Zbl

[16] V. V. Dodonov, “Nonclassical states in quantum optics: a “squeezed” review of the first 75 years”, J. Opt. B, 4:1 (2002), R1–R33 | MR

[17] A. O. Barut, L. Girardello, “New “Coherent States” Associated with Non-Compact Groups”, Commun. Math. Phys., 21:1 (1972), 41–55 | DOI | MR

[18] V. V. Borzov, E. V. Damaskinsky, “Coherent states for the Legendre oscillator”, Zap. Nauchn. Semin. POMI, 285, 2002, 39–52 | MR | Zbl

[19] V. V. Borzov, E. V. Damaskinskii, “Kogerentnye sostoyaniya i polinomy Chebysheva”, Trudy mezhdunarodnoi konferentsii “Matematicheskie idei P. L. Chebysheva i ikh prilozheniya k sovremennym problemam estestvoznaniya” (14–18 maya 2002), Obninsk

[20] V. V. Borzov, E. V. Damaskinsky, “Coherent states for Lagguere oscillator”, Day of Difraction, Procedings of the Workshop, SPb, 2002

[21] V. V. Borzov, E. V. Damaskinsky, “Barut–Girardello Coherent states for the Gegenbauer oscillator”, Zap. Nauchn. Semin. POMI, 291, 2002, 43–63 | MR | Zbl

[22] V. V. Borzov, “Orthogonal polynomials and generalized oscillator algebras”, Integral Transf. and Special Funct., 12:2 (2001), 115–138 | DOI | MR | Zbl

[23] V. V. Borzov, E. V. Damaskinsky, “Realization of the annihilation operator for generalized oscillator-like system by a differential operator”, Integral Transf. and Special Funct., 13 (2002), 1–8 | DOI | MR

[24] N. I. Akhiezer, Klassicheskaya problema momentov i nekotorye voprosy analiza, svyazannye s neyu, FM, Moskva, 1961

[25] V. V. Borzov, E. V. Damaskinsky, P. P. Kulish, “Construction of the spectral measure for the deformed oscillator position operator in the case of undetermined Hamburger moment problem”, Reviews in Math. Phys., 12:5 (2000), 691–710 | DOI | MR | Zbl

[26] J-M. Sixdenierrs, K. A. Penson, A. I. Solomon, “Mittag-Leffler coherent states”, J. Phys. A, 32:43 (1999), 7543–7563 | DOI | MR | Zbl