Superanalysis pp 183-225 | Cite as

Pseudodifferential Operators in Superanalysis

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


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.


Cauchy Problem Poisson Bracket Pseudodifferential Operator Pseudo Differential Operator Correspondence Principle 
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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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