Classes of bundles
Examples and Applications
A spinor bundle on a smooth manifold with spin structure is a -associated bundle associated to the spin group-principal bundle lifting the tangent bundle, for Vect a spin representation.
A section of a spinor bundle is called a spinor (a fermion field)
A Dirac operator acts on sections of a spinor bundle.
In physics, sections of spinor bundles model matter particles: fermion. See spinors in Yang-Mills theory.
standard model of particle physics and cosmology
Spinors in classical field theory (fermions):
Pierre Deligne, Daniel Freed, §3.4 of Classical field theory (1999) (pdf)
this is a chapter in
P. Deligne, P. Etingof, D.S. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D.R. Morrison, E. Witten (eds.) Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)
Discussion relating manifolds with spinor bundles to supergeometry includes
- B. L.Van derWaerden, Exclusion principle and spin, in Theoretical Physics in the Twentieth Century: A Memorial Volume to Wolfgang Pauli, ed. M. Fierz and V. F. Weisskopf, New York: Interscience, 1960
the name “spinor” is due to Paul Ehrenfest.
Revised on November 29, 2016 15:14:38
by Urs Schreiber