2014/08/18 by Atsushi Inoue, Inoue, Atsushi
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1408.3874
arxiv created 2014/08/18 · arxiv updated 2014/08/19
After introducing Berezin integral for polynomials of odd variables, we develop the elementary integral calculus based on supersmooth functions on the superspace \mathfrakRm|n. Here, \mathfrakR is the Fréchet-Grassmann algebra with countably infinite Grassmann generators, which plays the role of real number field ℝ. As is well-known that the formula of change of variables under integral sign is indispensable not only to treat PDE applying funtional analytic method but also to introduce analysis on supermanifolds. But, if we define naively the integral for supersmooth functions, there exists discrepancy which should be ameliorated. Here, we extend the contour integral modifying the parameter space introduced basically by de Witt, Rogers and Vladimirov and Volovich