Concept of Lie Derivative of Spinor Fields. A Geometric Motivated Approach
arXiv:1411.7845
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 £_{ξ}) is given by nice formulas when applied to Clifford and spinor fields, and moreoverl £_{ξ}g=0 for any vector field ξ. We compare our definitions and results with the many others appearing in literature on the subject.
20 pages. A preliminary version has been presented by W. A. Rodrigues Jr. at ICCA 10. In this version some important misprints are corrected