Multiloop QED in the Euler-Heisenberg approach

Abstract

I summarize what is known about the Euler-Heisenberg Lagrangian and its multiloop corrections for scalar and spinor QED, in various types of constant fields, and in various dimensions. Particular attention is given to the asymptotic properties of the weak-field expansion of the Lagrangian, which via Borel summation is related to Schwinger pair-creation, and the status of the "exponentiation conjecture" for the imaginary part of the Euler-Heisenberg to all loop orders.

Comments: 5 pages, 6 figures, talk given by C. Schubert at the Nineteenth Lomonosov Conference on Elementary Particle Physics, Moscow, August 22-28, 2019, to appear in the conference proceedings. arXiv admin note: substantial text overlap with arXiv:1807.05938