A Geometric Motivated Approach of Lie Derivative of Spinor Fields.

Abstract

In this paper using the Clifford bundle (C`(M, g)) and spin-Clifford bundle (C`Spine1,3 (M, g)) formalism, which permit to give a meaningfull representative of a Dirac-Hestenes spinor field (even section of C`Spine1,3 (M, g)) in the Clifford bundle, we give a geometrical motivated definition for the Lie derivative of spinor fields in a Lorentzian structure (M, g) where M is a manifold such that dim M = 4, g is Lorentzian of signature (1,3). Ours Lie derivative, called the spinor Lie derivative (and denoted £ξ ) is given by nice formulas swhen applied to Clifford and spinor fields, and moreover £ξ g = 0 for any vector field ξ. With this we compare our definitions and results in with the many others appearing in literature on the subject.