Realistic interpretation of Grassmann variables

Abstract

The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration of an exponential is due to the fact that the integral attains the known values only over a specific set of contours and not over their rescaled versions. Such contours live in infinite dimensional space and their sides are infinitesimal, and they make infinitely many turns. Finally, two different products are used: anticommutting wedge product and a Clifford dot product (the wedge product is used in the finite part of the integral and the Clifford dot product is used between the finite and infinitesimal parts). The integrals of non-analytic functions will become well-defined, although their specific value is unknown due to the various hidden parameters.

44 pages

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