Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity

Anatoly E. Shabad and Vladimir V. Usov
Phys. Rev. D 83, 105006 – Published 5 May 2011

Abstract

In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum c=1, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we establish the positive convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants that are derivatives of the effective Lagrangian with respect to the field invariants. Violation of the general principles by the one-loop approximation in QED at exponentially large magnetic field is analyzed, resulting in complex energy ghosts that signal the instability of the magnetized vacuum. Superluminal excitations (tachyons) appear, too, but for the magnetic field exceeding its instability threshold. Also other popular Lagrangians are tested to establish that the ones leading to spontaneous vacuum magnetization possess wrong convexity.

  • Received 8 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.105006

© 2011 American Physical Society

Authors & Affiliations

Anatoly E. Shabad1 and Vladimir V. Usov2

  • 1P.N. Lebedev Physics Institute, Moscow 117924, Russia
  • 2Center for Astrophysics, Weizmann Institute, Rehovot 76100, Israel

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Issue

Vol. 83, Iss. 10 — 15 May 2011

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