The construction of spinors in geometric algebra
- Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854 (United States)
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 Schrodinger-Pauli 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.
- OSTI ID:
- 20690162
- Journal Information:
- Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 317; ISSN 0003-4916; ISSN APNYA6
- Country of Publication:
- United States
- Language:
- English
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