Supermanifolds - Application to Supersymmetry

Pierre Cartier, Cecile DeWitt-Morette, Matthias Ihl, Christian Saemann, Maria bell

Research output: Chapter in Book/Report/Conference proceedingChapter

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.
Original languageEnglish
Title of host publicationMultiple facets of quantization and supersymmetry
EditorsM. A. Olshanetsky, Arkady Vainshtein
PublisherWorld Scientific Publishing
Publication statusPublished - 19 Feb 2002

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    Cartier, P., DeWitt-Morette, C., Ihl, M., Saemann, C., & bell, M. (2002). Supermanifolds - Application to Supersymmetry. In M. A. Olshanetsky, & A. Vainshtein (Eds.), Multiple facets of quantization and supersymmetry World Scientific Publishing.