International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69-72, Pages 3775-3781
doi:10.1155/S0161171204406565
The second-order Klein-Gordon field equation
D. Gomes1
and E. Capelas de Oliveira2
1Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria 97119-900, Rio Grande do Sul, Brazil
2Grupo de Física-Matemática, Faculdade de Ciências, Universidade de Lisboa, Lisboa 1649-003, Brazil
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.