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Superanalysis pp 183-225 | Cite as

Pseudodifferential Operators in Superanalysis

  • Andrei Khrennikov
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 470)

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 R n,m Λ 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.

Keywords

Cauchy Problem Poisson Bracket Pseudodifferential Operator Pseudo Differential Operator Correspondence Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Andrei Khrennikov
    • 1
    • 2
  1. 1.Department of Mathematics, Statistics and Computer SciencesUniversity of VäxjöVäxjöSweden
  2. 2.Department of MathematicsMoscow State University of Electronic EngineeringZelenogradRussia

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