Classifying Spinor Structures

Details Classifying Spinor Structures Classifying Spinor Structures

2001-06-10

arxiv.org/abs/math-ph/0106007v1

Physics

Mathematical Physics

Submitted as a thesis for consideration in the degree of Bachelor of Science with honours in Pure Mathematics at the Universit

Scientific paper

I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The central result of this thesis is a complete and constructive classification of spinor structures, generalising some earlier results. I will explain how principal fibre bundles and covering spaces provide the key ingredients to the proof. A different type of classification can also be attempted, in terms of the underlying principal fibre bundle, and this allows us to compare `spinor connections'. The final part indicates how spinor structures for Lorentzian manifolds provide the natural setting for the `spinor calculus', and so for the Dirac equation for the electron. The effect of the choice of spinor structure on the Dirac equation is investigated.

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