Gauge fields on coset spaces

Classical gauge theories are constructed on a class of associated bundlesS(M, G; G/A), with structure groupG, the fibre being isomorphic to a coset space ofG. An appropriate connection is found on such bundles. The connection supports a projective realization of the structure group. The connection coefficients may be identified as gauge potentials. This construction provides an example of gauge theories in which the number of independent gauge fields is smaller than the dimension of the local symmetry group