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All-Loop Result for the Strong Magnetic Field Limit of the Heisenberg-Euler Effective Lagrangian
1Helmholtz-Institut Jena, Fröbelstieg 3, 07743 Jena, Germany and Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany.
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.
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