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Foundations of analysis on superspace — 1: Differential calculus
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2015 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 7, no 2, 96-110 p.Article in journal (Refereed) Published
Abstract [en]

The recent experimental confirmation of the existence of Higgs boson stimulates theoretical research on supersymmetric models; in particular, mathematics of such modeling. Therefore we plan to present essentials of one special approach to “super-mathematics”, so called functional superanalysis (in the spirit of De Witt, Rogers, Vladimirov and Volovich, and the author of this review) in compact and clear form in series of review-type papers. This first paper is a review on super-differential calculus for the concrete model of the superspace (invented by Vladimirov and Volovich). In the next review we plan to present the integral supercalculus. The main distinguishing feature of functional superanalysis is that this is a real super-extension of analysis of Newton and Leibniz, opposite to algebraic models of Martin and Berezin. Here functions of commuting and anticommuting variables are no simply algebraic elements belonging to Grassmann algebras, but point-wise maps, from superspace into superspace. Finally, we remark that the first non-Archimedean physical model was based on invention by Vladimirov and Volovich of superspaces based on supercommutative Banach superalgebras over non-Archimedean (in particular, p-adic) fields. This model plays the basic role in theory of p-adic superstrings.

Place, publisher, year, edition, pages
Pleiades Publishing , 2015. Vol. 7, no 2, 96-110 p.
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:lnu:diva-51798DOI: 10.1134/S2070046615020028OAI: oai:DiVA.org:lnu-51798DiVA: diva2:916039
Available from: 2016-03-31 Created: 2016-03-31 Last updated: 2016-05-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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