Elementary features of Kaluza-Klein theories

Abstract

In many current uni cation theories involving gravity, it is natural to add compacti ed extra dimensions. To make a connection with our four-dimensional universe we need dimensional reduction to link a higher-dimensional theory to a lower-dimensional one. As a rst contact with the subject, we study how dimensional reduction works analyzing pure Einstein gravitation in D = d+1 dimensions, with an extra dimension compacti ed on S1. Finally, motivated by the presence of non- Abelian gauge groups in the Standard Model, we analyze extra dimensions compacti ed in some internal compact space, which give rise to gauge elds associated to these gauge groups.