On spinor bundles

Cartan Spinor Bundles on Manifolds. *

Cliiord Structures and Spinor Bundles

It is shown that every bundle ! M of complex, irreducible and faithful modules over the Cliiord bundle of an even-dimensional Riemannian space (M; g) with local model (V; h) is associated with a cpin (\Cliiord") structure on M, this being an extension of the SO(h)-bundle of orthonormal frames on M to the Cliiord group Cpin(h) = (C Spin(h))=Z 2. An explicit construction is given of the total spa...

Spin Spaces, Lipschitz Groups, and Spinor Bundles

It is shown that every bundle ! M of complex spinor modules over the Cliiord bundle Cl(g) of a Riemannian space (M; g) with local model (V; h) is associated with an lpin (\Lipschitz") structure on M, this being a reduction of the O(h)-bundle of all orthonormal frames on M to the Lips-chitz group Lpin(h) of all automorphisms of a suitably deened spin space. An explicit construction is given of t...

Conformal geometry of the supercotangent and spinor bundles

We study the actions of local conformal vector fieldsX ∈ conf(M, g) on the spinor bundle of (M, g) and on its classical counterpart: the supercotangent bundle M of (M, g). We first deal with the classical framework and determine the Hamiltonian lift of conf(M, g) to M. We then perform the geometric quantization of the supercotangent bundle of (M, g), which constructs the spinor bundle as the qu...

The Bundles of Algebraic and Dirac-Hestenes Spinor Fields

The main objective of this paper is to clarify the ontology of DiracHestenes spinor fields (DHSF ) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M =(M,g,∇, τg, ↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE ) in the case where M is a Lorentzian spacetime (the general case whe...