Concept of Lie Derivative of Spinor Fields. A Geometric Motivated Approach

Abstract

In this paper using the Clifford bundle (Cl(M,g)) and spin-Clifford bundle (Cl_{Spin_{1,3}^{e}}(M,g)) formalism, which permit to give a meaningfull representative of a Dirac-Hestenes spinor field (even section of Cl_{Spin_{1,3}^{e}}(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 dimM =4, g is Lorentzian of signature (1,3). Our Lie derivative, called the spinor Lie derivative (and denoted {\pounds}_{{\xi}}) is given by nice formulas when applied to Clifford and spinor fields, and moreoverl {\pounds}_{{\xi}}g=0 for any vector field {\xi}. We compare our definitions and results with the many others appearing in literature on the subject.