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Supermanifolds - Application to Supersymmetry

Pierre Cartier·Cecile DeWitt-Morette·Matthias Ihl·Christian Saemann·Maria E. Bell
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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.

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Pierre Cartier, Cecile DeWitt-Morette, Matthias Ihl, Christian Saemann, Maria E. Bell. 2002-02-19. Supermanifolds - Application to Supersymmetry. https://doi.org/10.1142/9789812777065_0029

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