Grassmann probatility, stochastic analysis, and applications

Borasi Luigi, Università di Milano (Statale)

We formulate a Grassmann (i.e. anticommuting) notion of probability theory and we describe some properties of Grassmann probability measures. We discuss stochastic analysis for Grassmann random variables including Gaussian processes, Brownian motion, and stochastic differential equations. Finally we sketch some applications to Euclidean quantum theories.

Area: CS33 - Measures, optimal transport and quantum systems (Francesco De Vecchi)

Keywords: Grassmann algebras, Euclidean Fermion fields, stochastic quantization, non-commutative probability, non-commutative stochastic partial differential equations, constructive quantum field theory.

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