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The goal of this paper is to define the Grassmann integral in terms of alimit of a sum around a well-defined contour so that Grassmann numbers gaingeometric meaning rather than symbols. The unusual rescaling properties of theintegration of an exponential is due to the fact that the integral attains theknown values only over a specific set of contours and not over their rescaledversions. Such contours live in infinite dimensional space and their sides areinfinitesimal, and they make infinitely many turns. Finally, two differentproducts are used: anticommutting wedge product and a Clifford dot product (thewedge product is used in the finite part of the integral and the Clifford dotproduct is used between the finite and infinitesimal parts). The integrals ofnon-analytic functions will become well-defined, although their specific valueis unknown due to the various hidden parameters.

Realistic interpretation of Grassmann variables