SU(1,1) coherent states for the Dunkl- Klein-Gordon equation in its canonical form

TL;DR

This paper constructs Perelomov coherent states for the Dunkl-Klein-Gordon equation using $rak{su}(1,1)$ symmetry, focusing on the even-parity sector and small curvature regime, with implications for curved space quantum mechanics.

Contribution

It introduces a novel construction of coherent states for the Dunkl-Klein-Gordon equation leveraging $rak{su}(1,1)$ symmetry, avoiding spin connections in curved space.

Findings

Coherent states are explicitly constructed for the Dunkl-Klein-Gordon equation.

Analysis is restricted to even-parity sector and small curvature regime.

The approach simplifies the equation by using a matrix-operator framework without spin connections.

Abstract

Using representation-theoretic techniques associated with the $\mathfrak{su}(1,1)$ symmetry algebra, we construct Perelomov coherent states for the Dunkl-Klein-Gordon equation in its canonical form, which is free of first-order Dunkl derivatives. Our analysis is restricted to the even-parity sector and to the regime where the curvature constant $R$ is much smaller than the system's kinetic energy. The equation under consideration emerges from a matrix-operator framework based on Dirac gamma matrices and a universal length scale that encodes the curvature of space via the Dunkl operator, thereby circumventing the need for spin connections in the Dirac equation.