Concept of Lie Derivative of Spinor Fields A Geometric Motivated Approach
Concept of Lie Derivative of Spinor Fields A Geometric Motivated Approach
复制标题
旋量场李导数的概念——一种几何激励方法
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
S. Wainer
中科院分区：
文献类型：
--
作者：
R. Leão;W. A. Rodrigues;S. Wainer
In this paper using the Clifford bundle ($${mathcal{C}ell(M,mathtt{g})}$$Cℓ(M,g)) and spin-Clifford bundle ($${mathcal{C}ell_{mathrm{Spin}_{1,3}^{e}} (M,mathtt{g})}$$CℓSpin1,3e(M,g)) formalism, which allow to give a meaningful representative of a Dirac-Hestenes spinor field (even section of $${mathcal{C}ell_{mathrm{Spin}_{1,3}^{e}}(M,mathtt{g})}$$CℓSpin1,3e(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). Our Lie derivative, called the spinor Lie derivative (and denoted $${overset{s}{pounds}_{oldsymbol{xi}}}$$£sξ) is given by nice formulas when applied to Clifford and spinor fields, and moreover $${overset{s}{pounds }_{{xi}}{oldsymbol {g}}=0}$$£sξg=0 for any vector field $${oldsymbol {xi}}$$ξ . We compare our definitions and results with the many others appearing in literature on the subject.
In this paper using the Clifford bundle ($${mathcal{C}ell(M,mathtt{g})}$$Cℓ(M,g)) and spin-Clifford bundle ($${mathcal{C}ell_{mathrm{Spin}_{1,3}^{e}} (M,mathtt{g})}$$CℓSpin1,3e(M,g)) formalism, which allow to give a meaningful representative of a Dirac-Hestenes spinor field (even section of $${mathcal{C}ell_{mathrm{Spin}_{1,3}^{e}}(M,mathtt{g})}$$CℓSpin1,3e(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). Our Lie derivative, called the spinor Lie derivative (and denoted $${overset{s}{pounds}_{oldsymbol{xi}}}$$£sξ) is given by nice formulas when applied to Clifford and spinor fields, and moreover $${overset{s}{pounds }_{{xi}}{oldsymbol {g}}=0}$$£sξg=0 for any vector field $${oldsymbol {xi}}$$ξ . We compare our definitions and results with the many others appearing in literature on the subject.