Symmetric spaces and Higgs models in the method of dimensional reduction. I. Potentials of the scalar fields of the reduced theory

Gauge models are studied which are obtained by means of dimensional reduction from pure gauge theories in multidimensional spaces of the type $M=M^4\times G/H$ where $G/H$ is a compact symmetric space. A general method of calculating scalar field potentials of the reduced theory is developed. The potentials turn out to be of the Higgs type.