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Mathematics Subject Classification: 97U60, 15A66.
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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.24 n.1 San José Jan./Jun. 2017
http://dx.doi.org/10.15517/rmta.v24i1.27749
Artículo
El fenómeno del espín semientero, cuaternios, y matrices de Pauli
The phenomenon of half-integer spin, quaternions, and Pauli matrices
1Escuela Agrícola Panamericana, Zamorano, Valle de Yeguare, F.M., Honduras y CICATA-Legaria, Instituto Politécnico Nacional, México D.F., CP 11500, México. E-Mail: fgonzalez@zamorano.edu
2CICATA-Legaria, Instituto Politécnico Nacional, México D.F., CP 11500, México. E-Mail: rigarcias2@ipn.mx
En este trabajo se reproduce el fenómeno del espín semientero de la ejemplificación que hizo Paul A. M. Dirac con un par de tijeras, una cuerda elástica y una silla. Se describen tres ejemplos más en el que aparece el mismo fenómeno y se relaciona la estructura algebraica de los cuaternios con uno de los ejemplos. Se describen los resultados básicos de las estructuras algebraicas de los cuaternios H, y se establece una relación intrínseca con el fenómeno espín semientero y las matrices de Pauli.
Palabras clave: Espín semientero; Cuaternios; matrices de Pauli; grupo fundamental
In this paper the phenomenon of half-integer spin exemplification Paul AM Dirac made with a pair of scissors, an elastic cord and chair play. Four examples in which the same phenomenon appears and the algebraic structure of quaternions is related to one of the examples are described.
[20]Mathematical proof of the phenomenon using known topological and algebraic results are explained. The basic results of algebraic structures are described quaternions H, and an intrinsic relationship with the phenomenon half-integer spin and the Pauli matrices is established.
Keywords: half-integer spin; quaternions; Pauli matrices; fundamental group
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Recibido: 03 de Marzo de 2016; Revisado: 16 de Agosto de 2016; Aprobado: 28 de Octubre de 2016
Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons
