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• W3100940887 abstract "We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method." @default.
• W3100940887 created "2020-11-23" @default.
• W3100940887 creator A5010501159 @default.
• W3100940887 creator A5031556014 @default.
• W3100940887 date "2020-11-13" @default.
• W3100940887 modified "2023-10-06" @default.
• W3100940887 title "Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces" @default.
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• W3100940887 doi "https://doi.org/10.3390/sym12111867" @default.
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