Finite Action Klein-Gordon Solutions on Lorentzian Manifolds
General Relativity and Quantum Cosmology
2007-05-23 v1 High Energy Physics - Theory
Mathematical Physics
Differential Geometry
math.MP
Abstract
The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein-Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.
Keywords
Cite
@article{arxiv.gr-qc/0603111,
title = {Finite Action Klein-Gordon Solutions on Lorentzian Manifolds},
author = {V. V. Kozlov and I. V. Volovich},
journal= {arXiv preprint arXiv:gr-qc/0603111},
year = {2007}
}
Comments
8 pages