2002/10/11 by Pavol Severa, Severa, Pavol
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #hep-th #math.QA #math.SG
paper · pdf · doi:10.48550/arxiv.math/0210169
4 pages; v2: minor changes
arxiv created 2003/07/29 · arxiv updated 2009/11/30
There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]=f,g for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical realization as a convolution algebra of the symplectic groupoid integrating the Poisson manifold. This quantization is just a part of a quantization of the odd symplectic category (where objects are odd symplectic supermanifolds and morphisms are Lagrangian relation) in terms of Z2-graded chain complexes. It is a straightforward consequence of the theory of BV operator acting on semidensities, due to H. Khudaverdian.