A new formulation of the effective theory for heavy particles

Abstract

We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the Wilson renormalization group transformation. The fixed point hamiltonian of our transformation coincides with the static hamiltonian and irrelevant operators can be identified with the usual $1/M$ corrections to the static theory. No matching condition has to be imposed between the full and the static theory operators with our approach. The values of the matching constants come out as a dynamical effect of the renormalization group flow.