Functional methods are generalized to two-loop EFT matching and running with manifest gauge covariance, and the hard-region matching formula is proven to all loop orders.
The Euler-Heisenberg Lagrangian beyond one loop
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abstract
We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue. The use of those corrections as a tool for the study of the properties of the QED perturbation series is outlined. As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg Lagrangian in 1+1 dimensional QED, obtained in the worldline formalism.
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A Guide to Functional Methods Beyond One-Loop Order
Functional methods are generalized to two-loop EFT matching and running with manifest gauge covariance, and the hard-region matching formula is proven to all loop orders.