p-Adic and Adelic Superanalysis
Branko Dragovich, Andrei Khrennikov
TL;DR
This paper explores the extension of superanalysis into p-adic and adelic frameworks, reviewing foundational concepts and illustrating with Grassmann algebra examples.
Contribution
It introduces the formulation of superalgebras and superanalysis over p-adic and adelic fields, expanding the mathematical tools for supersymmetric theories.
Findings
Development of p-adic and adelic superalgebras
Construction of superspaces over p-adic and adelic fields
Application of Grassmann algebra in superanalysis
Abstract
After a brief review of p-adic numbers, adeles and their functions, we consider real, p-adic and adelic superalgebras, superspaces and superanalyses. A concrete illustration is given by means of the Grassmann algebra generated by two anticommuting elements.
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Taxonomy
Topicsadvanced mathematical theories