Document Zbl 0413.58023

Models of Gross-Neveu type are quantization of a classical mechanics with nonlinear phase space. (English) Zbl 0413.58023

Commun. Math. Phys. 63, 131-153 (1978).

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MSC:

58J90	Applications of PDEs on manifolds
70H05	Hamilton’s equations
81S05	Commutation relations and statistics as related to quantum mechanics (general)
81T05	Axiomatic quantum field theory; operator algebras

Keywords:

Gross-Neveu type models; curved phase space; naturally canonically conjugated coordinates; field theoretical model

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Full Text: DOI

References:

[1]	Gross-Neveu, D.: Phys. Rev. D10, 3235 (1974) · doi:10.1103/PhysRevD.10.3235
[2]	Berezin, F.A.: Izv. Akad. Nauk SSr, Ser. Mat.38, 1116-1174 (1974); English translation: Math. USSR Izv.8, 1109-1165 (1974)
[3]	Berezin, F.A.: Izv. Akad. Nauk SSR, Ser. Mat.39, 363-402 (1975); English translation: Math. USSR Izv.9, 341-379 (1975)
[4]	Klauder, J.R.: J. Math. Phys.4, 1055 (1963) · Zbl 0127.18701 · doi:10.1063/1.1704034
[5]	Berezin, F.A.: Izv. Akad. Nauk SSR, Ser. Mat.36, 1134-1167 (1972); English translation: Math. USSR Izv.6, 1117-1151 (1972)
[6]	Berezin, F.A., Marinov, M.S.: Dynamics of a particle with half-integer spin as the Grassman version of classical mechanics. Preprint ITEP-43 (1976)
[7]	Hua Loo Keng: Harmonic analysis of the classical domain in the studi of analytic functions of several complex variables. Moskow: Inostrannaja Literatura 1959 (in Russian) · Zbl 0083.03601
[8]	Berezin, F.A.: Rep. Math. Phys.9, 15-30 (1976) · Zbl 0335.22014 · doi:10.1016/0034-4877(76)90014-8
[9]	Shereshevskiy, I.A.: Vestn. MGU (1977)
[10]	Berezin, F.A.: Metod vtorichnogo kvantovaniya. Moscow: Nauka 1965; English translation: Berezin, F.A.: The method of second quantization. New York-London: Academic Press 1966
[11]	Berezin, F.A.: Funct. Anal. Appl.1, 1-14 (1967) (in Russian) · doi:10.1007/BF01075861
[12]	Berezin, F.A.: Theor. Math. Phys.6, 194-211 (1971) (in Russian) · doi:10.1007/BF01036576
[13]	Gindikin, S.G.: Funct. Anal. Appl.9, 59-61 (1975) (in Russian) · Zbl 0332.32022 · doi:10.1007/BF01078179

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