An all-loop result for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian

Abstract

We provide an explicit expression for the strong magnetic field limit of the Heisenberg-Euler effective Lagrangian for both scalar and spinor quantum electrodynamics. To this end, we show that the strong magnetic field behavior is fully determined by one-particle reducible contributions discovered only recently. The latter can efficiently be constructed in an essentially algebraic procedure from lower-order one-particle reducible diagrams. Remarkably, the leading strong magnetic field behavior of the all-loop Heisenberg-Euler effective Lagrangian only requires input from the one-loop Lagrangian. Our result revises previous findings based exclusively on one-particle irreducible contributions. In addition we briefly discuss the strong electric field limit and comment on external field QED in the large $N$ limit.

5 pages, 2 figures; v2: differs from previous and published versions, correctly accounts for a factor of 1/2 in the 1PR contributions

References in corpus (10)

• The Schwinger mechanism revisited
• High magnetic fields for fundamental physics
• Exploring high-intensity QED at ELI
• An Addendum to the Heisenberg-Euler effective action beyond one loop
• One-particle reducible contribution to the one-loop spinor propagator in a constant field
• One-particle reducible contribution to the one-loop scalar propagator in a constant field
• Reducible contributions to quantum electrodynamics in external fields
• Three-loop Euler-Heisenberg Lagrangian in 1+1 QED, part 1: single fermion-loop part
• Tadpole diagrams in constant electromagnetic fields
• On the low-energy limit of the QED N-photon amplitudes: part 2

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