Conformal geometry of the supercotangent and spinor bundles

Jean-Philippe Michel (1)

1 ICJ - Institut Camille Jordan

We establish, via geometric quantization of the supercotangent bundle sM of (M,g), a correspondence between its conformal geometry and those of the spinor bundle. In particular, the Kosmann Lie derivative of spinors is obtained by quantization of the comoment map, associated to the new Hamiltonian action of conf(M,g) on sM. We study then the conf(M,g)-module structures induced on the space of differential operators acting on spinor densities and on its spaces of symbols (functions on sM). In the conformally flat case, we classify their conformal invariants, including the conformally odd powers of the Dirac operator.

Mots clés: Conformal geometry; Symplectic supermanifold; Spin geometry; Geometric quantization; Conformally invariant differential operators; Conformal geometry

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Jean-Philippe Michel. Conformal geometry of the supercotangent and spinor bundles. 2010. ⟨hal-00472224⟩