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Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
Rev.colomb.mat. v.42 n.2 Bogotá jul./dic. 2008
1Universidad de Los Andes, Bogotá, Colombia. Email: dbatic@uniandes.edu.co
2Universidad de Los Andes, Bogotá, Colombia. Email: Harald.Schmid@UBH.de
In this paper we compute the square root of the generalized squared total angular momentum operator J for a Dirac particle in the Kerr-Newman metric. The separation constant λ arising from the Chandrasekahr separation ansatz turns out to be the eigenvalue of J. After proving that J is a symmetry operator, we show the completeness of Chandrasekhar ansatz for the Dirac equation in oblate spheroidal coordinates and derive an explicit formula for the time evolution operator e-itH.
Key words: Dirac equation, Kerr-Newman metric, general relativity.
2000 Mathematics Subject Classification: 83C57, 47B15, 47B25.
En este trabajo derivamos la raíz cuadrada del operador generalizado del momento angular para una partícula de Dirac en la métrica de Kerr-Newman. La constante de separación λ introducida por el ansatz de Chandrasekhar resulta ser el valor propio de J. Después de haber mostrado que J es un operador de simetría, probamos la completitud del ansatz de Chandrasekhar para la ecuación de Dirac en coordenadas esferoidales oblongas y derivamos una expresión analítica para el operador de evolución temporal e-itH.
Palabras clave: Ecuación de Dirac, métrica de Kerr-Newman, relatividad general.
Texto completo disponible en PDF
References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv42n2a06,
AUTHOR = {Batic, Davide and Schmid, Harald},
TITLE = {{Chandrasekhar ansatz and the generalized total angular momentum operator for the Dirac equation in the Kerr-Newman metric}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2008},
volume = {42},
number = {2},
pages = {183-207}
}