The Dirac equation is separated, by separation of variables, in the Schwarzschild space-time. The radial equations are reduced to a pair of decoupled ordinary differential equations of the second order. Asymptotic behaviours of the radial solutions are determined. A covariant scalar product between states is considered that is induced by the conserved current. It is shown that a class of states exist that are bound with respect to the scalar product. The states characterized by asymptotic polynomial-like behaviour are associated to a Hydrogen-like energy spectrum.

Spin 1/2 Bound States in Schwarzschild Geometry / A. Zecca. - In: ADVANCED STUDIES IN THEORETICAL PHYSICS. - ISSN 1313-1311. - 1:5-8(2007), pp. 271-279.

Spin 1/2 Bound States in Schwarzschild Geometry

A. Zecca
2007

Abstract

The Dirac equation is separated, by separation of variables, in the Schwarzschild space-time. The radial equations are reduced to a pair of decoupled ordinary differential equations of the second order. Asymptotic behaviours of the radial solutions are determined. A covariant scalar product between states is considered that is induced by the conserved current. It is shown that a class of states exist that are bound with respect to the scalar product. The states characterized by asymptotic polynomial-like behaviour are associated to a Hydrogen-like energy spectrum.
Schwarzschild space-time; Dirac equation;solution; product of states; bound states
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
http://www.m-hikari.com/astp/astp2007/astp5-8-2007/zeccaASTP5-8-2007.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/34264
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