English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is shown in the present paper that the transformation relating a paralleltransported vector in a Weyl space to the original one is the product of amultiplicative gauge transformation and a proper orthochronous Lorentztransformation. Such a Lorentz transformation admits a spinor representation,which is obtained and used to deduce the transportation properties of a Weylspinor, which are then expressed in terms of a composite gauge group defined asthe product of a multiplicative gauge group and the spinor group. Theseproperties render a spinor amenable to its treatment as a particle coupled to amultidimensional gauge field in the framework of the Kaluza-Klein formulationextended to multidimensional gauge fields. In this framework, a fiber bundle isconstructed with a horizontal, base space and a vertical, gauge space, which isa Lie group manifold, termed its structure group. For the present, the base isthe Minkowski spacetime and the vertical space is the composite gauge groupmentioned above. The fiber bundle is equipped with a Riemannian structure,which is used to obtain the classical description of motion of a spinor. In itsclassical picture, a Weyl spinor is found to behave as a spinning chargedparticle in translational motion. The corresponding quantum description isdeduced from the Klein-Gordon equation in the Riemann spaces obtained by themethods of path-integration. This equation in the present fiber bundle reducesto the equation for a spinor in the Weyl geometry, which is close to butdiffers somewhat from the squared Dirac equation.

Formulation of spinors in terms of gauge fields