Abstract
All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike.
Highlights
All nonlinear extensions of the source-free Maxwell equations preserving both SOð2Þ electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalization of Born-Infeld electrodynamics
The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarization
It is to be expected that any nonlinear electrodynamics theory in a Minkowski spacetime will have some conformal weak-field limit, and it is established that this must be Maxwell electrodynamics if it is assumed that all conformal invariant equations arise as Euler-Lagrange (EL) equations for a Lagrangian density that is a real analytic function of gauge-invariant Lorentz scalars constructed from electric and magnetic fields only
Summary
All nonlinear extensions of the source-free Maxwell equations preserving both SOð2Þ electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalization of Born-Infeld electrodynamics. It is to be expected that any nonlinear electrodynamics theory in a Minkowski spacetime will have some conformal weak-field limit, and it is established that this must be Maxwell electrodynamics if it is assumed that all conformal invariant equations arise as Euler-Lagrange (EL) equations for a Lagrangian density that is a real analytic function of gauge-invariant Lorentz scalars constructed from electric and magnetic fields only This assumption implies that the only possible conformal strong-field limit is Maxwell’s theory, whereas the strong-field limit of BI theory has long been known to be an interacting conformal theory [4,5], which we shall call Bialynicki-Birula (BB) electrodynamics. It has implications for predictions derived from the Euler-Heisenberg theory, as we explain in our conclusions
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