摘要: Let us consider a Lie (super)algebra G spanned by Tα where are quantum observables in BV formalism. It is proved that for every tensor cα...α determines homology class of the algebra expression cα...αTα...Tα again observable. This theorem used to construct sigma model. We apply this construction explain Kontsevich's results about relation between Hamiltonian vector fields and topological invariants manifolds.
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Maxim Kontsevich, Feynman Diagrams and Low-Dimensional Topology Birkhäuser Basel. pp. 97- 121 ,(1994) , 10.1007/978-3-0348-9112-7_5
Scott Axelrod, I. M. Singer, Chern-Simons perturbation theory. II Journal of Differential Geometry. ,vol. 39, pp. 173- 213 ,(1994) , 10.4310/JDG/1214454681
A. S. Schwarz, The partition function of a degenerate functional Communications in Mathematical Physics. ,vol. 67, pp. 1- 16 ,(1979) , 10.1007/BF01223197
Albert Schwarz, Symmetry transformations in Batalin-Vilkovisky formalism Letters in Mathematical Physics. ,vol. 31, pp. 299- 301 ,(1994) , 10.1007/BF00762792
A.S. Schwarz, Yu.S. Tyupkin, Quantization of antisymmetric tensors and ray-singer torsion Nuclear Physics. ,vol. 242, pp. 436- 446 ,(1984) , 10.1016/0550-3213(84)90403-6
I. A. Batalin, G. A. Vilkovisky, Quantization of gauge theories with linearly dependent generators Physical Review D. ,vol. 28, pp. 2567- 2582 ,(1983) , 10.1103/PHYSREVD.28.2567
M. Kontsevich, A. Schwarz, M. Alexandrov, O. Zaboronsky, The Geometry of the Master Equation and Topological Quantum Field Theory International Journal of Modern Physics A. ,vol. 12, pp. 1405- 1429 ,(1997) , 10.1142/S0217751X97001031
Albert Schwarz, Geometry of Batalin-Vilkovisky quantization Communications in Mathematical Physics. ,vol. 155, pp. 249- 260 ,(1993) , 10.1007/BF02097392