The canonical bundle is a one complex dimensional subbundle of the bundle formula_52 of complex differential forms on "M". Recall that the gamma matrices define an isomorphism between differential forms and spinors. In particular even and odd forms map to the two chiralities of Weyl spinors. Vectors have an action on differential forms given by the interior product. One-forms have an action on forms given by the wedge product. Thus sections of the bundle formula_51 act on differential forms. This action is a representation of the action of the Clifford algebra on spinors.