Dirac Operator on the Quantum Sphere

Abstract

We construct a Dirac operator on the quantum sphere $S_q^2$ which is covariant under the action of $S{U}_q(2)$. 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 $S{U}_q(2)$ invariant field theories on $S_q^2$ following the Connes-Lott approach to noncommutative geometry.

13 pages

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