We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Plebanski. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing stationary points in which the field strength acquires a nonzero vacuum expectation value. The associated spontaneous breaking of Lorentz symmetry can in principle be detected by coupling the model to a suitable external current, or to gravity. We show that the possible vacua can be classified in four classes. We study some of their properties, using explicit examples for illustration.
تحميل البحث