The Dirac particle on central backgrounds and the anti-de Sitter oscillator

Details The Dirac particle on central backgrounds and the anti-de Sitter oscillator The Dirac particle on central backgrounds and the anti-de Sitter oscillator

1998-03-12

arxiv.org/abs/gr-qc/9803042v1

Mod.Phys.Lett.A13:2923-2936,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, Latex

Scientific paper

10.1142/S0217732398003107

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so that the spherical coordinates can be separated in terms of angular spinors like in special relativity, obtaining a pair of radial equations and a specific form of the radial scalar product. As an example, we analytically solve the anti-de Sitter oscillator giving the formula of the energy levels and the form of the corresponding eigenspinors.

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