The Quantum Deformed Dirac Equation from the k-Poincare` Algebra

TL;DR

This paper derives a deformed Dirac equation invariant under the k-Poincare` algebra, linking it to the second Casimir, and explores its spinorial realization via contraction of SO_q(3,2).

Contribution

It introduces a new deformed Dirac equation invariant under the k-Poincare` algebra and connects it to the second Casimir, expanding the understanding of quantum-deformed relativistic equations.

Findings

Deformed Dirac equation invariant under k-Poincare` algebra.

Relation between the square of the k-Dirac operator and the second Casimir.

Spinorial realization obtained via contraction of SO_q(3,2).

Abstract

In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski vector). The ``spinorial'' realization of the k-Poincare` is obtained by a contraction of the coproduct of the real form of SO_q(3,2) using the 4-dimensional representation which results to be, up some scalar factors, the same of the undeformed algebra in terms of the usual gamma matrices.