Classifying Spinor Structures
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:mathph/0106007
 Bibcode:
 2001math.ph...6007M
 Keywords:

 Mathematical Physics;
 Mathematics  Differential Geometry;
 Mathematics  Mathematical Physics;
 53C10;
 53C27;
 83C60
 EPrint:
 Submitted as a thesis for consideration in the degree of Bachelor of Science with honours in Pure Mathematics at the University of New South Wales, Australia