2-Spinors via Linear Algebra

2022/04/27 by Roger Plymen, Plymen, Roger
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.2204.12842

Abstract

We give a streamlined account of 2-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles SL₂(ℂ) ×_SU2 S and SL₂(ℂ) ×_SU2 S. A solution of the Dirac equation determines a pair of conjugate 2-spinor fields over the mass shell X_m.

Related

• Classifying Spinor Structures
• An introduction to spinors
• Part I: Vector Analysis of Spinors
• On the spinor formalism for even n
• On operator fields in the bundle of Dirac spinors