General internal gauge symmetry

A theory is outlined in which $n$ scalar field interact in a way that is invariant under all real, nonsingular local linear transformations of the mesons among themselves. The energy of the system is positive. The symmetry spontaneously breaks down to a compact subgroup of GL($n,R$)and the gauge mesons of the broken symmetry become massive. Their longitudinal components are supplied by the derivatives of an internal metric tensor with which no physical particles are associated.