Dirac operators on quantum two spheres

TL;DR

This paper constructs a covariant Dirac operator for spin-1/2 fermions on quantum two spheres, utilizing quantum group symmetries and q-analogs of Pauli matrices, advancing the understanding of quantum geometry.

Contribution

It introduces a covariant Dirac operator on quantum two spheres and formulates fermion wave functions respecting quantum group symmetries.

Findings

Wave functions constructed in a covariant manner

Dirac operator expressed using q-analogs of Pauli matrices

Framework for fermions on quantum spheres established

Abstract

We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$. The concept of total angular momentum and chirality can be expressed by using $q$-analog of Pauli-matrices and appropriate commutation relations.