Changes of variables and the renormalization group

A class of exact infinitesimal renormalization group (RG) transformations is studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a saddle point approximation is more accurate, becoming, in some cases, asymptotically exact as the transformations are iterated. The formalism provides a simplified and unified approach to several known renormalization groups. The RG equations for a scalar field theory are obtained and solved both by expanding in epsilon = d-4 and also by expanding in a single coupling constant. This calculation yields results in agreement with conventional methods. Next the application is studied of this kind of RG to Yang-Mills theories. A simple exact gauge covariant RG transformation is constructed; the corresponding RG equations are obtained and solved in the weak coupling regime. A lattice gauge theory is proposed for which the application of this RG formalism is straightforward