SPINORS AND GRAVITATIONAL FIELD
Résumé
Spinors have been used in Particle Physics since the Dirac's equation. However their physical meaning is still obscure. In this paper we show that Spinors, vectors of a 4 dimensional complex vector space, can be used to represent the kinematic characteristics of particles,, encompassing both their transversal and their rotational parts. The framework used is the geometry of General Relativity, which is presented in a comprehensive and consistent way, with fiber bundles. Spinors can be can be used at any scale, and the definition of a deformable solid body is introduced. The gravitational field is treated as a gauge field, through a connection on a fiber bundle. Using the spinor representation, the action of the gravitation field on a material body, with the covariant derivative, takes then a simple form. The propagation of the field is studied by a two form valued in the Lie algebra, similar to the Riemann tensor. In this formulation, more general but fully compatible with the more traditional approach starting from the metric and the scalar curvature, the structure of the gravita-tional field can be explored, showing the existence of a rotational and a transversal component, and quantized, the spin being similar to the usual 3 dimensional gravity.
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