Supermanifolds - Application to Supersymmetry
Cartier, Pierre ; DeWitt-Morette, Cecile ; Ihl, Matthias ; Saemann, Christian ; Bell, Maria E.
arXiv, 0202026 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2002-02-19
Classification:  Mathematical Physics,  High Energy Physics - Theory 
@article{0202026,
     author = {Cartier, Pierre and DeWitt-Morette, Cecile and Ihl, Matthias and Saemann, Christian and Bell, Maria E.},
     title = {Supermanifolds - Application to Supersymmetry},
     journal = {arXiv},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0202026}
}

Cartier, Pierre; DeWitt-Morette, Cecile; Ihl, Matthias; Saemann, Christian; Bell, Maria E. Supermanifolds - Application to Supersymmetry. arXiv, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/0202026/