Large N external-field quantum electrodynamics

We advocate the study of external-field quantum electrodynamics with N charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large N limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large N Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonstrate that further analytical insights are possible for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field and work out the all-orders strong field limit of the theory.

Automated summary

This article advocates the study of external-field quantum electrodynamics with N charged particle flavors. The focus is on the Heisenberg-Euler effective action in the large N limit, considering contributions from all loop orders. The results show that beyond one loop, the contributions are generated by the one-loop Heisenberg-Euler effective Lagrangian, providing an explicit determination of the large N Heisenberg-Euler effective action at any desired loop order. Further insights are provided for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field, and the all-orders strong field limit of the theory is derived.