Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background (1112.6192v1)

Published 28 Dec 2011 in hep-th, gr-qc, math-ph, and math.MP

Abstract: 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 dS⁴ 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 dS⁴ is imaginary: m² being proportional to -N(N+3), with N >= 0 an integer.

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