Trace Anomaly in Strong Electromagnetic Fields

Violation of the superposition principle in the Maxwell field could arise from intrinsic nonlinearity in the fundamental theory of the photon, such as seen in Born-Infeld (BI) electrodynamics, but certainly occurs due to charged particle vacuum fluctuations, i.e. one-loop quantum electrodynamics (QED). The necessary presence of a dimensioned scale in a nonlinear theory induces a nonvanishing trace in the energy-momentum tensor $$ T_{\mu}^{\mu} = -M\frac{d L_{\rm eff}}{dM} = -4\left(L_{\rm eff}-\mathcal{S} \frac{\it \partial L_{\rm eff}}{\partial S} - P \frac{\it \partial L_{\rm eff}}{\partial P}\right), \quad $$ where $\mathcal{S,P}$ are the scalar and pseudo scalar field invariants. $T_{\mu}^{\mu}$ has the form of the Einstein cosmological constant, and hence intense electromagnetic fields generate a localized, dark energy-like concentration.\\[0.2cm] References: \\ {\it Trace Anomaly of Nonlinear Electrodynamics and its (Anti)\ Gravitational Effect} arXiv:0811.4467 [hep-th] and \\ {\it QED Conformal Anomaly in External Fields} arXiv:0810.1323 [hep-ph]