Super differential calculus
About: This article is published in Osaka Journal of Mathematics. The article was published on 01 Jan 1988. and is currently open access. The article focuses on the topics: Time-scale calculus & Differential calculus.
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Citations
A partial solution for feynman's problem: a new derivation of the weyl equation
Atsushi Inoue
- 01 Jan 2000
TL;DR: In this article, the authors give a procedure for Feynman type quantization of a Schrodinger type equation with spin and a good parametrization for the Weyl equation with an external electro-magnetic field.
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An extension of the method of characteristic to a system of Partial Differential Operators-- an application to the Weyl equation with external field by "Super Hamiltonian path-integral method"
TL;DR: In this article, a Fourier Integral Operator with matrix-like phase and amplitude functions was constructed for the super Weyl equation on the superspace, which is a parametrization of the classical Weyl equations on the Euclidian space.
2
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Remarks on elementary integral calculus for supersmooth functions on superspace ${\mathfrak{R}}^{m|n}$
TL;DR: In this paper, the elementary integral calculus based on supersmooth functions on the superspace was developed, which is the Fr\'echet-Grassmann algebra with countably infinite Grassmann generators and plays the role of real number field.
References
The theory of G∞ supermanifolds
Charles P. Boyer,Samuel Gitler +1 more
TL;DR: In this article, a theory of supervarietes is proposed, in which a super-variete is a variete ordinaire associee of a G-structure.
47
Homogeneous spaces of infinite-dimensional lie algebras and characteristic classes of foliations
I N Bernshtein,B I Rozenfel'd +1 more
TL;DR: Gel'fand as mentioned in this paper introduced a new language to describe many problems of differential geometry: for example, problems connected with the theory of pseudogroups, Lie equations, foliations, characteristic classes.
A Global Theory of Supermanifolds
Abstract: A mathematically rigorous definition of a global supermanifold is given. This forms an appropriate model for a global version of superspace, and a class of functions is defined which corresponds to superfields. This new construction is compared with several pre‐existing definitions of supermanifold and graded manifold; it is shown to include all these definitions and to go beyond them, particularly in admitting the possibility of nontrivial topology in the anticommuting sector. Local differential geometry and potential applications to supergravity are considered.