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

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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.

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Authors and Affiliations

  1. Lebedev Physical Institute, RAS, Moscow, Russia

    I. A. Batalin

  2. Tomsk State Pedagogical University, Tomsk, Russia

    P. M. Lavrov

Authors
  1. I. A. Batalin
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  2. P. M. Lavrov
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Corresponding author

Correspondence to I. A. Batalin.

Additional information

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).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 2, pp. 200–212, May, 2016.

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Batalin, I.A., Lavrov, P.M. Conversion of second-class constraints and resolving the zero-curvature conditions in the geometric quantization theory. Theor Math Phys 187, 621–632 (2016). https://doi.org/10.1134/S0040577916050020

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