Feeds:
Posts
From Lawson-Michelson:  Suppose $X$ is a spin manifold with a spin structure on its tangent bundle.  Let $S$ be any spinor bundle associated to $T(X)$.  Then $S$ is a bundle of modules over $Cl(X)$, carries a canonical riemannian connection.  The Dirac operator in this case was first written down by Atiyah and Singer in their work on the Index Theorem.  Finding the operator was a major accomplishment so Lawson-Michelson call it the Atiyah-Singer operator.