Ja n 19 99 Spin spaces , Lipschitz groups , and spinor bundles

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...

Verlinde spaces and Prym theta functions

1 Introduction The Verlinde formula is a remarkable—and potentially very useful—new tool in the geometry of algebraic curves which is borrowed from conformal field theory. In the first instance it is a trigonometric expression which assigns a natural number N l (G, g) to data consisting of a semisimple algebraic group G, a nonnegative integer g and an auxiliary integer l ∈ Z. In physics N l (G,...

ar X iv : q - a lg / 9 41 20 06 v 1 1 9 D ec 1 99 4 CLASSICAL SPINOR STRUCTURES ON QUANTUM SPACES

A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular, analogs of the Dirac operator and the Laplacian are introduced and analyzed. A general construction of examples of quantum spaces with a spinor structure is presented.

Differentiation along Multivector Fields

The Lie derivation of multivector fields along multivector fields has been introduced by Schouten (see cite{Sc, S}), and studdied for example in cite{M} and cite{I}. In the present paper we define the Lie derivation of differential forms along multivector fields, and we extend this concept to covariant derivation on tangent bundles and vector bundles, and find natural relations between them and...

Ja n 19 99 I . ELECTRON AND PROTON SPIN POLARISATION IN STORAGE RINGS —