Linearized five dimensional Kaluza–Klein theory as a gauge theory
G. Atondo–Rubio, J.A. Nieto*, L. Ruiz, and J. Silvas
Facultad de Ciencias Físico–Matemáticas, Universidad Autónoma de Sinaloa, 80000, Culiacán, Sinaloa, México, * e–mail: nieto@uas.uasnet.mx
Recibido el 30 de julio de 2007
Aceptado el 26 de marzo de 2008
Abstract
We develop a linearized five–dimensional Kaluza–Klein theory as a gauge theory. By perturbing the metric around flat and de Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular case of five dimensions, we show that in using the Kaluza–Klein mechanism, the field equations of our approach imply both linearized gauge gravity and Maxwell theory in flat and de Sitter scenarios. As a possible further development of our formalism, we also discuss an application in the context of gravitational polarization scattering by means of the analogue of the Mueller matrix in optical polarization algebra. We argue that this application can be of particular interest in gravitational wave experiments.
Keywords: Kaluza–Klein theory; linearized gravity; Mueller matrix
Resumen
Desarrollamos una teoría Kaluza–Klein linealizada en cinco dimensiones como una teoría de norma. Discutimos primero gravedad linealizada como una teoría de norma en cualquier dimensión perturbando las métricas de fondo plana y la de de Sitter. Demostramos que usando el mecanismo de Kaluza–Klein en el caso particular de cinco dimensiones, las ecuaciones de campo de nuestra aproximación implican tanto gravedad linealizada de norma como la teoría de Maxwell en escenarios planos y de de Sitter. Como otro posible desarrollo de nuestro formalismo, también discutimos una aplicación en el contexto de dispersión gravitacional polarizada, por medio de una matriz análoga a la de Mueller usada en el álgebra de polarización óptica. Argumentamos que esta aplicación puede ser de interés particular en los experimentos de ondas gravitacionales.
Descriptores: Teoría de Kaluza–Klein; gravedad linealizada; matriz de Mueller.
PACS: 04.50.+h, 04.30.–w, 98.80.–k, 42.15.–i
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Acknowledgments
We would like to thank C.M. Yee and E.A. León for their helpful comments. This work was supported in part by the UAS under the program PROFAPI–2006.
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