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**Superanalogs of symplectic and contact geometry and their applications to quantum field theory.**
*(English)*
Zbl 0873.58004

Dobrushin, R. L. (ed.) et al., Topics in statistical and theoretical physics. F. A. Berezin memorial volume. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 177(32), 203-218 (1996).

Summary: The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field theory. In particular, regarding \(N\)-superconformal geometry as a particular case of contact complex geometry, one can better understand \(N=2\) superconformal field theory and its relationship to topological conformal field theory. Odd symplectic geometry constitutes a mathematical basis of the Batalin-Vilkovisky procedure for the quantization of gauge theories.

The exposition is mostly based on published papers. However, the paper also contains a review of some unpublished results (in the section devoted to the axiomatics of \(N=2\) superconformal theory and to topological quantum field theory).

For the entire collection see [Zbl 0853.00022].

The exposition is mostly based on published papers. However, the paper also contains a review of some unpublished results (in the section devoted to the axiomatics of \(N=2\) superconformal theory and to topological quantum field theory).

For the entire collection see [Zbl 0853.00022].

### MSC:

58A50 | Supermanifolds and graded manifolds |

53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |

81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |