Building Grassmann Numbers from PI-Algebras
Ricardo M. Bentin, Sergio Mota
TL;DR
This paper explores the mathematical foundation of Grassmann Numbers in theoretical physics by constructing them using Polynomial Identity Algebras, enhancing understanding of Berezin integration.
Contribution
It introduces a novel approach to derive Grassmann Numbers from PI-Algebras, linking algebraic structures to physical concepts.
Findings
Establishes a formal link between Grassmann Numbers and PI-Algebras.
Provides a new algebraic framework for Berezin integration.
Enhances mathematical understanding of Grassmann algebra in physics.
Abstract
This works deals with the formal mathematical structure of so called Grassmann Numbers applied to Theoretical Physics, which is a basic concept on Berezin integration. To achieve this purpose we make use of some constructions from relative modern Polynomial Identity Algebras (PI-Algebras) applied to the special case of the Grassmann algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Logic