Katharina Habermann, Andreas Klein
Lie derivative of symplectic spinor fields, metaplectic representation, and quantization
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 57, 71-91(2003)

MSC:

81S10 Geometric quantization, symplectic methods, See Also {

53C80 Applications to physics

Abstract: In the context of Riemannian spin geometry it requires skilful handling to
define a Lie derivative of (Riemannian) spinor fields.

A Lie derivative of symplectic spinor fields in the direction of Hamiltonian
vector fields can be defined in a very natural way.
It is the aim of this note to present this construction.
Furthermore, an immediate interpretation of this Lie derivative
in the language of natural ordering quantization is given.

Keywords: Geometry and quantization, symplectic methods; Applications to physics