1998/03/27 by Semyon Pol'shin, Pol'shin, Semyon
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Crystallography and Radiation Phenomena #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #advanced mathematical theories #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9803092
This paper has been withdrawn since its main results now explained in hep-th/0001040 and hep-th/0001069
openalex publication_date 1998/03/27 · arxiv created 2000/01/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.