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Finite Action Klein-Gordon Solutions on Lorentzian Manifolds

V. V. Kozlov·I. V. Volovich
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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.

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V. V. Kozlov, I. V. Volovich. 2006-03-28. Finite Action Klein-Gordon Solutions on Lorentzian Manifolds. https://arxiv.org/abs/gr-qc/0603111

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