Dynamical mass generation in QED with magnetic fields: arbitrary field strength and coupling constant

摘要

We study the dynamical generation of masses for fundamental fermions inquenched quantum electrodynamics, in the presence of magnetic fields ofarbitrary strength, by solving the Schwinger-Dyson equation (SDE) for thefermion self-energy in the rainbow approximation. We employ the Rituseigenfunction formalism which provides a neat solution to the technical problemof summing over all Landau levels. It is well known that magnetic fieldscatalyze the generation of fermion mass m for arbitrarily small values ofelectromagnetic coupling \alpha. For intense fields it is also well known thatm \propto \sqrt eB. Our approach allows us to span all regimes of parameters\alpha and eB. We find that m \propto \sqrt eB provided \alpha is small.However, when \alpha increases beyond the critical value \alpha_c which marksthe onslaught of dynamical fermion masses in vacuum, we find m \propto \Lambda,the cut-off required to regularize the ultraviolet divergences. Our methodpermits us to verify the results available in literature for the limiting casesof eB and \alpha. We also point out the relevance of our work for possiblephysical applications.