Multiloop Information from the QED Effective Lagrangian

Abstract

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.

8 pages, to appear in the proceedings of IX Mexican Workshop on Particles and Fields, Colima, Nov 17-22, 2003

Cited by in corpus (10)

• Thermal Schwinger pair production at arbitrary coupling
• On the Higher Loop Euler-Heisenberg Trans-Series Structure
• Identifying Time Scales in Particle Production from Fields
• String-inspired representations of photon/gluon amplitudes
• Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop
• Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Schwinger Pair Creation of Particles and Strings
• Photon-Graviton Amplitudes from the Effective Action