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Concept of Lie Derivative of Spinor Fields A Geometric Motivated Approach

2015; Birkhäuser; Volume: 27; Issue: 1 Linguagem: Inglês

10.1007/s00006-015-0560-y

1661-4909

Rafael F. Leão, Waldyr A. Rodrigues, Samuel A. Wainer,

Mathematics and Applications

In this paper using the Clifford bundle ( $${\mathcal{C}\ell(M,\mathtt{g})}$$ ) and spin-Clifford bundle ( $${\mathcal{C}\ell_{\mathrm{Spin}_{1,3}^{e}} (M,\mathtt{g})}$$ ) formalism, which allow to give a meaningful representative of a Dirac-Hestenes spinor field (even section of $${\mathcal{C}\ell_{\mathrm{Spin}_{1,3}^{e}}(M,\mathtt{g})}$$ ) 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). Our Lie derivative, called the spinor Lie derivative (and denoted $${\overset{s}{\pounds}_{\boldsymbol{\xi}}}$$ ) is given by nice formulas when applied to Clifford and spinor fields, and moreover $${\overset{s}{\pounds }_{{\xi}}{\boldsymbol {g}}=0}$$ for any vector field $${\boldsymbol {\xi}}$$ . We compare our definitions and results with the many others appearing in literature on the subject.