The construction of spinors in geometric algebra
Abstract
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some real geometric algebra, the gap among algebraic, geometric, and physical methods is closed. Spinors are developed in any number of dimensions from a discussion of spin groups, followed by the specific cases of U (1), SU (2), and SL(2,C) spinors. The physical observables in SchrödingerPauli theory and Dirac theory are found, and the relationship between Dirac, Lorentz, Weyl, and Majorana spinors is made explicit. The use of a real geometric algebra, as opposed to one defined over the complex numbers, provides a simpler construction and advantages of conceptual and theoretical clarity not available in other approaches.
 Publication:

Annals of Physics
 Pub Date:
 June 2005
 DOI:
 10.1016/j.aop.2004.11.008
 arXiv:
 arXiv:mathph/0403040
 Bibcode:
 2005AnPhy.317..383F
 Keywords:

 02.20.Sv;
 02.40.Hw;
 Lie algebras of Lie groups;
 Classical differential geometry;
 Mathematical Physics
 EPrint:
 20 pages, 1 figure