Abstract
In this chapter we expose the theory of PDO on a superspace over topological CSM. These superspaces can have a finite as well as infinite number of supercoordinates. Thus, the proposed PDO calculus serves as a mathematical basis for the quantization of physical supersystems with a finite as well as infinite number degrees of freedom. In a finite-dimensional case, we obtain quantum mechanics on the superspace Rn,mΛ and in an infinite-dimensional case we obtain a quantum theory of a superfield, in particular, that of a superstring and superstring field, and fermion theories and boson theories with anticommuting Faddeev-Popov ghosts.
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© 1999 Springer Science+Business Media Dordrecht
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Khrennikov, A. (1999). Pseudodifferential Operators in Superanalysis. In: Superanalysis. Mathematics and Its Applications, vol 470. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4609-8_5
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DOI: https://doi.org/10.1007/978-94-011-4609-8_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5948-0
Online ISBN: 978-94-011-4609-8
eBook Packages: Springer Book Archive