Spinor calculus for q-deformed quantum spaces I

TL;DR

This paper develops a framework for q-deformed spinor calculus, introducing q-analogs of Pauli matrices and Fierz identities, and explores their properties and relations in quantum spaces relevant to physics.

Contribution

It introduces q-analogs of Pauli matrices and Fierz identities, extending spinor calculus to q-deformed quantum spaces for the first time.

Findings

Q-analogs of Pauli matrices are constructed and analyzed.

Key properties and relations of q-deformed spinor calculus are established.

Foundations for physical applications in quantum space models are provided.

Abstract

The article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and higher-dimensional quantum spaces like the q-deformed Euclidean space in four dimensions or the q-deformed Minkowski space is outlined. These considerations are continued by introducing q-analogs of the Pauli matrices. Their main properties are discussed in detail and numerous relations that could prove useful in physical applications are presented. In this respect, q-deformed versions of the important Fierz identities are written down.