1994/06/17 by Albert Schwarz, Schwarz, Albert
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.hep-th/9406120
openalex publication_date 1994/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 particular case of contact complex geometry, one can better understand N=2 superconformal field theory and its connection to topological conformal field theory. The odd symplectic geometry constitutes a mathematical basis of Batalin-Vilkovisky procedure of quantization of gauge theories. The exposition is based mostly on published papers. However, the paper contains also a review of some unpublished results (in the section devoted to the axiomatics of N=2 superconformal theory and topological quantum field theory). The paper will be published in Berezin memorial volume.