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.Pubblicazioni consigliate
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