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

TL;DR

This paper investigates the properties of the effective Lagrangian in nonlinear electrodynamics, focusing on causality and unitarity, and analyzes the stability and physical consistency of various models under strong magnetic fields.

Contribution

It establishes the convexity and positivity conditions of the effective Lagrangian and examines violations leading to instabilities and superluminal phenomena in quantum electrodynamics.

Findings

Convexity of the effective Lagrangian is confirmed for constant fields.

Violations at high magnetic fields lead to complex ghosts and vacuum instability.

Models with spontaneous vacuum magnetization exhibit incorrect convexity.

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 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.