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Geometry of spin 1/2 particles

Resumen
Inglés
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.
Palabras clave: Bra-ket formalism, geometric algebra, spacetime algebra, Schr¨odinger-Pauli equation, Dirac equation, Dirac-Hestenes equation, spinor, spinor operator.
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Sistema de Información Científica Redalyc
Red de Revistas Científicas de América Latina y el Caribe, España y Portugal
Universidad Autónoma del Estado de México
Versión 2.2 beta | 2015
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