Dynamical mass generation: from elementary fields to bound states

Abstract

We investigate the dynamical generation of fermion mass in Quantum Electrodynamics (QED) and in Quantum Chromodynamics (QCD). This non-perturbative study is performed using a truncated set of Schwinger-Dyson equations for the fermion and photon propagator and the quark propagator. First, we study dynamical fermion mass generation in QED using a cancellation mechanism for the full photon-electron vertex that respects multiplicative renor- malisability and reproduces perturbation theory and determine the critical coupling in different approximations. We then study the quark equation using a model for the strong coupling with two parameters and compare this study with previous ones. Finally, we show how bound states masses derived by lattice calculations can be extrapolated to low quark masses using the Nambu Jona-Lasinio model (NJL) and demonstrate the limitation of the NJL model. As an outlook, we present a functional method to control the quantum fluctuations of a given theory. We derive an exact equation for the effective action T and using a gradient expansion for T we derive evolution equations for different couplings.