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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| 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 |
| 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. |
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