# A use of geometric calculus to reduce Berezin integral to the limit of a Riemann sum

Thomas Scanlon, Roman Sverdlov

Arxiv ID: 0908.2605•Last updated: 6/19/2020

Berezin integration of functions of anticommuting Grassmann variables is
usually seen as a formal operation, sometimes even defined via differentiation.
Using the formalism of geometric algebra and geometric calculus in which the
Grassmann numbers are endowed with a second associative product coming from a
Clifford algebra structure, we show how Berezin integrals can be realized in
the high dimensional limit as integrals in the sense of geometric calculus. We
then show how the concepts of spinors and superspace transform into this
framework.

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