Supermanifolds - Application to Supersymmetry
Abstract
Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships between the different definitions of supermanifolds proposed by various people. In addition, we work with four complexes allowing an invariant definition of divergence: - an ascending complex of forms, and a descending complex of densities on real variables - an ascending complex of forms, and descending complex of densities on Grass mann variables. This study is a step towards an invariant definition of integrals of superfunctions defined on supermanifolds leading to an extension to infinite dimensions. An application is given to a construction of supersymmetric Fock spaces.
Cite
@article{arxiv.math-ph/0202026,
title = {Supermanifolds - Application to Supersymmetry},
author = {Pierre Cartier and Cecile DeWitt-Morette and Matthias Ihl and Christian Saemann and Maria E. Bell},
journal= {arXiv preprint arXiv:math-ph/0202026},
year = {2016}
}
Comments
to appear in the "Michael Marinov Memorial Volume"