Dirac Operator on the Quantum Sphere

A. Pinzul, A. Stern

Published 2001-03-23, updated 2001-04-02Version 3

We construct a Dirac operator on the quantum sphere $S^2_q$ which is covariant under the action of $SU_q(2)$. It reduces to Watamuras' Dirac operator on the fuzzy sphere when $q\to 1$. We argue that our Dirac operator may be useful in constructing $SU_q(2)$ invariant field theories on $S^2_q$ following the Connes-Lott approach to noncommutative geometry.