Geometry of spin 1/2 particles
2015; Mexican Society of Physics; Volume: 61; Issue: 3 Linguagem: Inglês
ISSN
2683-2224
Autores Tópico(s)Noncommutative and Quantum Gravity Theories
ResumoThe 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
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