Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

Details Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

2000-03-28

arxiv.org/abs/hep-th/0003253v2

Phys.Rev. D62 (2000) 085009

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1 Figure, RevTeX; the manuscript has been substantially revised and enlarged in order to make it selfcontained; acce

Scientific paper

10.1103/PhysRevD.62.085009

Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory like QED in 3+1 dimensions. We take as trial action a general retarded quadratic action both for the bosonic and fermionic degrees of freedom and derive the variational equations for the corresponding retardation functions. We find a simple analytic, non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that gamma_m(alpha) becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no obvious sign of the chiral symmetry breaking observed in calculations based on the use of Dyson-Schwinger equations, however we find that a perturbative expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we investigate the behaviour of gamma_m(alpha) at large orders in perturbation theory.

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