Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-03-27
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
This paper has been withdrawn since its main results now explained in hep-th/0001040 and hep-th/0001069
Scientific paper
The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible representations are constructed. The explicit solutions of these equations possessing a simplicity and physical transparency are obtained without use of the separation of variables method. The connection with the general-covariant approach to wave equations in a curved space is established. It is shown that the Anti-de Sitter space is the solution of the Einstein-Dirac equations. The geometrical meaning of the mass quantization in the Anti-de Sitter space and of the particle creation in de Sitter space is shown.
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