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Analysis on superspace: an overview

Published online by Cambridge University Press:  17 April 2009

Vladimir G. Pestov
Vladimir G. Pestov
Affiliation:
Department of MathematicsVictoria University of WellingtonWellingtonNew Zealand e-mail: vladimir.pestov@vuw.ac.nz
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Abstract

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The concept of superspace is fundamental for some recent physical theories, notably supersymmetry, and a mathematical feedback for it is provided by superanalysis and supergeometry. We survey the state of affairs in superanalysis, shifting our attention from supermanifold theory to “plain” superspaces. The two principal existing approaches to superspaces are sketched and links between them discussed. We examine a problem by Manin of representing even geometry (analysis) as a collective effect in infinite-dimensional purely odd geometry (analysis), by applying the technique of nonstandard (infinitesimal) analysis.

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Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 135 - 165
Copyright
Copyright © Australian Mathematical Society 1994

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