International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 710864 | https://doi.org/10.1155/S0161171204406565

D. Gomes, E. Capelas De Oliveira, "The second-order Klein-Gordon field equation", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 710864, 7 pages, 2004. https://doi.org/10.1155/S0161171204406565

The second-order Klein-Gordon field equation

Received22 Jun 2004

Abstract

We introduce and discuss the generalized Klein-Gordon second-order partial differential equation in the Robertson-Walker space-time, using the Casimir second-order invariant operator written in hyperspherical coordinates. The de Sitter and anti-de Sitter space-times are recovered by means of a convenient choice of the parameter associated to the space-time curvature. As an application, we discuss a few properties of the solutions. We also discuss the case where we have positive frequency exponentials and the creation and annihilation operators of particles with known quantum numbers. Finally, we recover the Minkowskian case, that is, the case of null curvature.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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