Relativistic description of constituent quarks

Abstract

In this paper we propose a formalism to remove the center of mass motion of the relativistic three-quark system in order to calculate not only one-body operators, but also two-body interactions. We employ various methods used in the past to remove the center of mass motion. We then calculate the masses of the nucleon and \ensuremath{\Delta} resonance with residual one-gluon, sigma meson, and pseudoscalar pion and eta meson exchange potentials. Magnetic moments, root mean square radii, pion-nucleon coupling constant, and the axial vector coupling constant are also calculated. The main purpose of the calculation is to study the effect of the removal of the center of mass motion and investigate the similarities and differences between a relativistic and nonrelativistic description of constituent quarks. The method projecting onto the total momentum $P=0,$ is found to give results consistent with experiments. It is also found that light quark mass and strong confinement are appropriate to reproduce the nucleon and \ensuremath{\Delta} masses in the relativistic approach.