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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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Universidad Autónoma del Estado de México
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Versión 3.0 | 2017