Nucleon dynamics in effective field theory of nuclear forces

Abstract

Low energy nucleon dynamics in the effective field theory (EFT) of nuclear forces is investigated by using the formalism of the generalized quantum dynamics (GQD). This formalism is based on a generalized dynamical equation derived as the most general equation of motion consistent with the current concepts of quantum theory and allows one to extend quantum dynamics to the case where the fundamental interaction in a quantum system is nonlocal in time. The Schr{ö}dinger equation follows from this equation in the case where the interaction in a system is instantaneous. We show that the effective theory of nuclear forces gives rise to low energy nucleon dynamics which is governed by the generalized dynamical equation with a nonlocal-in-time interaction operator. This operator is shown to provide a natural parametrization of the interaction of nucleons and can be derived order by order by using methods of subtractive EFT's. We show that the use of the GQD for describing nucleon dynamics allows one to formulate the EFT of nuclear forces as a completely consistent theory with a well-defined equation of motion which does not require renormalization.