标题： 代数旋量场和Dirac-Hestenes旋量场的束 显示英文标题

标题： The Bundles of Algebraic and Dirac-Hestenes Spinor Fields

摘要： 本文的主要目的是阐明狄拉克-赫斯廷斯旋量场（DHSF）的本体论及其与一般允许自旋结构的黎曼-卡特时空中的偶数多向量场之和的关系，并给出当时空为洛伦兹时空时所谓的狄拉克-赫斯廷斯方程（DHE）的一个严格的数学推导。 为此，我们引入了多向量场的 Clifford 丛（Cl(M,g)）以及自旋流形 (M,g) 上的左（Cl_{自旋_{1,3}^{e}}^{l}(M)）和右（Cl_{自旋_{1,3}^{e}}^{r}(M)）自旋-Clifford 丛。 明确了左理想代数旋量场（LIASF）与狄拉克-赫斯廷斯旋量场之间的关系（这两种场都是 Cl_{自旋_{1,3}^{e}}^{l}(M) 的截面）。 我们详细研究了 Clifford 场和左右自旋-Clifford 场的协变导数理论。 此外，我们在洛伦兹时空上找到了一个一致的狄拉克方程（记作 DECl^{l}）用于 DHSF。 我们也成功地得到了 DECl^{l}在 Clifford 丛 Cl(M,g) 中的一个表示。 我们称这样的方程为 DHE，并且它被偶数多向量场（EMFS）所满足。 当然，这样的 EMFS 不是一个旋量场。 此外，我们还提供了一种关于 Clifford 场和各种旋量场协变导数的一致理论。 我们强调，尽管 DECl^{l}和 DHE 有关联，但它们具有不同的数学性质。 我们还研究了局部洛伦兹不变性和电磁规范不变性，并表明只有对于 DHE 这些变换具有相同的数学性质，从而暗示它们之间可能存在某种联系。 显示英文摘要

摘要： The main objective of this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF) and its relationship with sum of even multivector fields, on a general Riemann-Cartan spacetime admitting a spin structure and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE) when spacetime is a Lorentzian. To this aim we introduce the Clifford bundle of multivector fields (Cl(M,g)) and the left (Cl_{Spin_{1,3}^{e}}^{l}(M)) and right (Cl_{Spin_{1,3}^{e}}^{r}(M)) spin-Clifford bundles on the spin manifold (M,g) The relation between left ideal algebraic spinor fields (LIASF) and Dirac-Hestenes spinor fields (both fields are sections of Cl_{Spin_{1,3}^{e}}^{l}(M)) is clarified. We study in details the theory of the covariant derivatives of Clifford and left and right spin-Clifford fields. Moreover, we find a consistent Dirac equation for a DHSF (denoted DECl^{l}) on a Lorentzian spacetime. We succeeded also in obtaining a representation of the DECl^{l} in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by even multivector fields (EMFS). Of course, such a EMFS is not a spinor field. We provide moreover a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DECl^{l} and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the electromagnetic gauge invariance and show that only for the DHE such transformations are of the same mathematical nature, thus suggesting a possible link between them.