Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-09-02
J.Phys.Conf.Ser. 37 (2006) 59-72
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, to appear in the proceedings of IX Mexican Workshop on Particles and Fields, Colima, Nov 17-22, 2003
Scientific paper
We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.
Dunne Gerald V.
Schubert Christian
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