Generalized Fierz Identities and the Superselection Rule for Geometric Multispinors

Details Generalized Fierz Identities and the Superselection Rule for Geometric Multispinors Generalized Fierz Identities and the Superselection Rule for Geometric Multispinors

1992-11-14

arxiv.org/abs/gr-qc/9211018v2

Spinors, Twistors, Clifford Algebras and Quantum Deformations (Proceedings of the Second Max Born Symposium, Wroclaw, Poland,

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, Eliminated use of non-standard LaTeX macros, a square root of \rho added in last line of paragraph below equation 2,

Scientific paper

The inverse problem, to reconstruct the general multivector wave function from the observable quadratic densities, is solved for 3D geometric algebra. It is found that operators which are applied to the right side of the wave function must be considered, and the standard Fierz identities do not necessarily hold except in restricted situations, corresponding to the spin-isospin superselection rule. The Greider idempotent and Hestenes quaterionic spinors are included as extreme cases of a single superselection parameter.

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