On Hierarchy and Equivalence of Relativistic Equations for Massive Fields

Details On Hierarchy and Equivalence of Relativistic Equations for Massive Fields On Hierarchy and Equivalence of Relativistic Equations for Massive Fields

2009-07-27

arxiv.org/abs/0907.4736v2

Grav.Cosmol.14:53-59,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, twocolumn. Problem of construction the hierarchy of solutions in the massive case reformulated

Scientific paper

10.1134/S0202289308010076

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for different spins and on the origin of spinor transformations. In particular, starting from a solution to the Dirac equation, one obtains a chain of other solutions to both Dirac and Klein-Gordon equations. A comparison with the massless case is performed, and examples of non-trivial singular solutions are presented. A generalization to Riemannian space-time and inclusion of interactions are briefly discussed.

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