Geodesic
Conversion of second-class constraints and resolving the~zero-curvature conditions in the~geometric quantization theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 200-212

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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. 
@article{TMF_2016_187_2_a0,
     author = {I. A. Batalin and P. M. Lavrov},
     title = {Conversion of second-class constraints and resolving the~zero-curvature conditions in the~geometric quantization theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {200--212},
     publisher = {mathdoc},
     volume = {187},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a0/}
}
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I. A. Batalin; P. M. Lavrov. Conversion of second-class constraints and resolving the~zero-curvature conditions in the~geometric quantization theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 200-212. http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a0/