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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 2, Pages 200–212
DOI: https://doi.org/10.4213/tmf9007
(Mi tmf9007)
 

This article is cited in 1 scientific paper (total in 1 paper)

Conversion of second-class constraints and resolving the zero-curvature conditions in the geometric quantization theory

I. A. Batalina, P. M. Lavrovb

a Lebedev Physical Institute, RAS, Moscow, Russia
b Tomsk State Pedagogical University, Tomsk, Russia
Full-text PDF (400 kB) Citations (1)
References:
Abstract: In the approach to geometric quantization based on the conversion of second-class constraints, we resolve the corresponding nonlinear zero-curvature conditions for the extended symplectic potential. From the zero-curvature conditions, we deduce new linear equations for the extended symplectic potential. We show that solutions of the new linear equations also satisfy the zero-curvature condition. We present a functional solution of these new linear equations and obtain the corresponding path integral representation. We investigate the general case of a phase superspace where boson and fermion coordinates are present on an equal basis.
Keywords: symplectic potential, second-class constraint, conversion method.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00489
14-02-01171
Ministry of Education and Science of the Russian Federation З.867.2014/К
The research of I. A. Batalin is supported in part by the Russian Foundation for Basic Research (Grant Nos. 14-01-00489 and 14-02-01171). The research of P. M. Lavrov is supported by the Ministry of Education and Science of the Russian Federation (Project No. Z.867.2014/K).
Received: 17.07.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 2, Pages 621–632
DOI: https://doi.org/10.1134/S0040577916050020
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. A. Batalin, P. M. Lavrov, “Conversion of second-class constraints and resolving the zero-curvature conditions in the geometric quantization theory”, TMF, 187:2 (2016), 200–212; Theoret. and Math. Phys., 187:2 (2016), 621–632
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9007
  • https://doi.org/10.4213/tmf9007
  • https://www.mathnet.ru/eng/tmf/v187/i2/p200
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:282
    Full-text PDF :130
    References:49
    First page:18
     
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