On the Dimensions of the Chiral and Dilatation Symmetry Breaking Hamiltonian Densities

Denoting by l_u and l_δ the dimensions (if any) of the chiral and dilation symmetry breaking Hamiltonian densities u(x) and δ(x), respectively, the property (4 – l_u) (l_u – l_δ) > 0 (which is already known in special cases) is derived for a much larger class of models. We furthermore obtain a simple and general explicit expression for u(x) in terms of the current divergences, and review the physical applications of this (or an analogous, almost obvious) expression.