Geometry of spin 1/2 particles

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 repr...

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Bibliographic Details
Author: G. Sobczyk
Format: article
Status:Published version
Publication Date:2015
Country:México
Institution:Universidad de las Américas Puebla
Repository:Redalyc-UDLAP
OAI Identifier:oai:redalyc.org:57038074009
Online Access:https://www.redalyc.org/articulo.oa?id=57038074009
Access Level:Open access
Keyword:Física, Astronomía y Matemáticas
Bra
Dirac
spinor
Schr¨odinger
ket formalism
Description
Summary: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.