Current structure of phenomenological Lagrangians

It is shown that phenomenological Lagrangians that are invariant with respect to a group $G$ are representable as products of currents when they are realized on homogeneous (with respect to transformations of $G$) irreducible symmetric spaces $G/H$. In the case of general homogeneous spaces the requirement that a phenomenological Lagrangian be representable as a product of currents can be satisfied only if the phenomenological constants are chosen in a definite manner. In certain cases this corresponds to an enlargement of the symmetry group of the original Lagrangian.