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Foundations of analysis on superspace — 1: Differential calculus

On finite-temperature string field theory and p-adic string

Application of p-Adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into ℚ$_{ p }$

On spaces extremal for the Gomory-Hu inequality

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Foundations of analysis on superspace — 1: Differential calculus

Content Provider	Springer Nature Link
Author	Khrennikov, A. Yu.
Copyright Year	2015
Abstract	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.
Starting Page	96
Ending Page	110
Page Count	15
File Format	PDF
ISSN	20700466
Journal	P-Adic Numbers, Ultrametric Analysis, and Applications
Volume Number	7
Issue Number	2
e-ISSN	20700474
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-05-07
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	supersymmetry superspace Banach superalgebra superanalysis Algebra
Content Type	Text
Resource Type	Article
Subject	Mathematics

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A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

Cohomology of osp(2|2) acting on spaces of linear differential operators on the superspace ℝ$^{1|2}$

Differential algebras and simple Jordan superalgebras

A Differential Calculus on Z3-Graded Quantum Superspace ${\mathbb R}_{q}(2|1)$

$${\mathfrak {osp}}(2|2)$$ -Trivial deformations of modules of weighted densities on the superspace $${\mathbb {R}}^{1|2}$$

Noncommutative differential calculus on a quadratic algebra

On differential properties of mappings into a Banach space

Extension of the Weierstrass factorization theorem

Exterior calculus of Lie superalgebra valued differential forms on superspace

Foundations of analysis on superspace — 1: Differential calculus

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A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

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A Differential Calculus on Z3-Graded Quantum Superspace ${\mathbb R}_{q}(2|1)$

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Foundations of analysis on superspace — 1: Differential calculus