Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-06-30
Int.J.Mod.Phys.A19:2217-2232,2004
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, Latex. Submitted to Phys.Rev. D
Scientific paper
10.1142/S0217751X04017690
It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the transformations of the isometry group so that the generalized spherical coordinates can be separated in terms of angular spinors like in the flat case, obtaining a pair of radial equations. In this approach the equation of the free field Dirac in $AdS_{d+1}$ backgrounds is analytically solved obtaining the formula of the energy levels and the corresponding normalized eigenspinors.
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