A Geometric Motivated Approach of Lie Derivative of Spinor Fields.

Authors

  • Rafael de Freitas Leão
  • Waldyr Alves Rodrigues Jr.
  • Samuel Augusto Wainer

DOI:

https://doi.org/10.5540/03.2017.005.01.0206

Keywords:

Lie Derivative, Spinor Fields, Dirac-Hestenes Spinor Fields, Clifford Fiber Bundle, Spin-Clifford Fiber Bundle.

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.

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Published

2017-04-14

Issue

Section

Trabalhos Completos - Matemática Aplicada à Física