The Construction of Spinors in Geometric Algebra
arXiv:math-ph/0403040 · doi:10.1016/j.aop.2004.11.008
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 between 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 , $\SU(2)$, and spinors. The physical observables in Schrödinger-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.
20 pages, 1 figure
References in corpus (1)
Cited by in corpus (15)
- From Dirac spinor fields to ELKO
- From Dirac Action to ELKO Action
- Revealing how different spinors can be: the Lounesto spinor classification
- How should spin-weighted spherical functions be defined?
- Geometric (Clifford) algebra and its applications
- Dimensional scaffolding of electromagnetism using geometric algebra
- Deformed Geometric Algebra and Supersymmetric Quantum Mechanics
- Two-State Quantum Systems Revisited: a Geometric Algebra Approach
- Real spinors and real Dirac equation
- Spin Description in the Star Product and the Path Integral Formalism
- Geometric Algebra and Star Products on the Phase Space
- On Computable Geometric Expressions in Quantum Theory
- Notes on the Dynamics of Noncommutative U(2) and Commutative SU(3) Instantons
- A key to the projective model of homogeneous metric spaces
- Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra