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Chandrasekhar ansatz and the generalized total angular momentum operator for the Dirac equation in the Kerr-Newman metric
El ansatz de Chandrasekhar y el operador generalizado del momento angular para la ecuación de Dirac en la métrica de Kerr-Newman
Palabras clave:
Dirac equation, Kerr-Newman metric, general relativity, 2000 Mathematics Subject Classification. 83C57, 47B15, 47B25 (en)Ecuación de Dirac, métrica de Kerr-Newman, relatividad general (es)
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Abstract. 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.
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.
Referencias
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