Nonperturbative mass renormalization in quenched QED from the worldline variational approach - art. no. 085009

Following Feynman's successful treatment of the polaron problem we apply th e same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectori es, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory such as QED in 3 1 dimensions. We take as a trial action a general retarded quadratic actio n both for the bosonic and fermionic degrees of freedom and derive the vari ational equations for the corresponding retardation functions. We find a si mple analytic, non-perturbative, solution for the anomalous mass dimension gamma (m)(alpha) in the MS scheme. For small couplings we compare our resul t with recent four-loop perturbative calculations while at large couplings we find that gamma (m)(alpha) becomes proportional to root alpha. The anoma lous mass dimension shows no obvious sign of the chiral symmetry breaking o bserved in calculations based on the use of Dyson-Schwinger equations: howe ver, we find that a-perturbative expansion of gamma (m)(alpha) diverges for alpha >0.7934. Finally, we investigate the behavior of gamma (m)(alpha) at large orders in perturbation theory.