Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background

Details Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background

2011-12-28

arxiv.org/abs/1112.6192v1

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 4 figures

Scientific paper

Using methods in the theory of semisimple Lie algebras, we can obtain all smooth solutions of the Klein-Gordon equation on the 4-dimensional de Sitter spacetime (dS^4). The mass of a Klein-Gordon scalar on dS^4 is related to an eigenvalue of the Casimir operator of so(1,4). Thus it is discrete, or quantized. Furthermore, the mass m of a Klein-Gordon scalar on dS^4 is imaginary: m^2 being proportional to -N(N+3), with N >= 0 an integer.

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