Superanalysis on quantum spaces

TL;DR

This paper develops superanalysis tools like Grassmann integrals and exponentials for antisymmetrised quantum spaces such as Manin plane, q-deformed Euclidean, and Minkowski spaces, enhancing mathematical frameworks in quantum physics.

Contribution

It introduces q-analogs of superanalysis elements specifically tailored for antisymmetrised quantum spaces, expanding the mathematical toolkit for quantum physics applications.

Findings

Constructed q-analogs for Grassmann integrals and exponentials

Extended superanalysis to q-deformed Euclidean and Minkowski spaces

Provided braided products with supernumbers in quantum spaces

Abstract

Attention is focused on antisymmetrised versions of quantum spaces that are of particular importance in physics, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each of these quantum spaces we provide q-analogs for elements of superanalysis, i.e. Grassmann integrals, Grassmann exponentials, Grassmann translations and braided products with supernumbers.