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Group Theoretical Examination of the Relativistic Wave Equations on Curved Spaces. II. De Sitter and Anti-de Sitter Spaces

Semyon Pol'shin
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Abstract

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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Semyon Pol'shin. 2000-01-12. Group Theoretical Examination of the Relativistic Wave Equations on Curved Spaces. II. De Sitter and Anti-de Sitter Spaces. https://arxiv.org/abs/gr-qc/9803092

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