On Hierarchy and Equivalence of Relativistic Equations for Massive Fields
General Relativity and Quantum Cosmology
2010-11-23 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.0907.4736,
title = {On Hierarchy and Equivalence of Relativistic Equations for Massive Fields},
author = {Vladimir V. Kassandrov},
journal= {arXiv preprint arXiv:0907.4736},
year = {2010}
}
Comments
7 pages, twocolumn. Problem of construction the hierarchy of solutions in the massive case reformulated