Stable magnetic Lorentz-violating vacua in gauge-invariant nonlinear electrodynamics

Abstract We investigate gauge-invariant nonlinear electrodynamics in the Plebański first-order Hamiltonian formulation, taking the single-invariant potential $\hat{V}(P)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mover mml:miV</mml:mi> mml:mo^</mml:mo> </mml:mover> mml:mrow mml:mo(</mml:mo> mml:miP</mml:mi> mml:mo)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> as the primary object. Our focus is on the existence of stable Lorentz-violating magnetic v