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Multiloop Euler-Heisenberg Lagrangians, Schwinger pair creation, and the photon S-matrix. (English. Russian original) Zbl 1382.81226
Russ. Phys. J. 59, No. 11, 1746-1751 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 59, No. 11, 23-27 (2016).
Summary: Although the perturbation series in quantum electrodynamics has been studied for eighty years concerning its high-order behavior, our present understanding is still poorer than for many other field theories. An interesting case is Schwinger pair creation in a constant electric field, which may possibly provide a window to high loop orders; simple non-perturbative closed-form expressions have been conjectured for the pair creation rate in the weak field limit, for scalar QED in 1982 by Affleck, Alvarez, and Manton, and for spinor QED by Lebedev and Ritus in 1984. Using Borel analysis, these can be used to obtain non-perturbative information on the on-shell renormalized $$N$$-photon amplitudes at large $$N$$ and low energy. This line of reasoning also leads to a number of nontrivial predictions for the effective QED Lagrangian in either four or two dimensions at any loop order, and preliminary results of a calculation of the three-loop Euler-Heisenberg Lagrangian in two dimensions are presented.

##### MSC:
 81V10 Electromagnetic interaction; quantum electrodynamics 81T18 Feynman diagrams 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 81R25 Spinor and twistor methods applied to problems in quantum theory
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##### References:
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