B 2017

Odd Scalar Curvature in Batalin-Vilkovisky Geometry

BERING LARSEN, Klaus

Basic information

Original name

Odd Scalar Curvature in Batalin-Vilkovisky Geometry

Authors

Edition

Brno, Czech Republic, 36 pp. 2017

Publisher

Habilitation thesis, Masaryk University

Other information

Language

English

Type of outcome

Odborná kniha

Field of Study

10303 Particles and field physics

Country of publisher

Czech Republic

Confidentiality degree

není předmětem státního či obchodního tajemství

Organization unit

Faculty of Science

Keywords in English

Supermathematics; Supermanifolds; Odd Poisson Geometry; Darboux Theorem; Antibracket; Batalin-Vilkovisky Geometry; Curvature;

Tags

Změněno: 17/3/2019 16:22, doc. Klaus Bering Larsen, Ph.D.

Abstract

V originále

After a brief introduction to Batalin-Vilkovisky (BV) formalism, we treat aspects of supermathematics in algebra and differential geometry, such as, stratification theorems, Frobenius theorem and Darboux theorem on supermanifolds. We use Weinstein's splitting principle to prove Darboux theorem for regular, possible degenerate, even and odd Poisson supermanifolds. Khudaverdian's nilpotent operator (which takes semidensities into semidensities of opposite Grassmann-parity) is introduced on both (i) an atlas of Darboux coordinates and (ii) in arbitrary coordinates. An odd scalar function is defined and it is shown that it has a geometric interpretation as an odd scalar curvature.

Links

GBP201/12/G028, research and development project
Name: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku
Investor: Czech Science Foundation