Geometry of spin 1/2 particles

• Autores: Garret Sobczyk
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 61, Nº. 3, 2015, págs. 211-223
• Idioma: inglés
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• Resumen

  • The geometric algebras of space and spacetime are derived by sucessively extending the real number system to include new mutually anticommuting square roots of +/-1. The quantum mechanics of spin 1/2 particles are then expressed in these geometric algebras. Classical 2 and 4 component spinors are represented by geometric numbers which have parity, providing new insight into the familiar bra-ket formalism of Dirac. The classical Dirac Equation is shown to be equivalent to the Dirac-Hestenes equation, so long as the issue of parity is not taken into consideration, the latter quantity being constructed in such a way that it is parity invarient.