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- Standing wave solutions in Born-Infeld theoryPublication . Manojlovic, Nenad; Perlick, Volker; Potting, RobertusWe study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. the problem then reduces to solving the scalar Born-Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born-Infeld equation: an iterative method, and a "minimal surface" method. We also study standing wave solutions in a uniform constant magnetic field background. the results obtained in this work provide a theoretical background for experimental tests of Born-Infeld theory. (C) 2020 Elsevier Inc. All rights reserved.
- Degenerate behavior in nonlinear vacuum electrodynamicsPublication . Escobar, C. A.; Potting, RobertusWe study nonlinear vacuum electrodynamics in the first-order formulation proposed by Plebanski. We analyze in detail the equations of motion, and identify conditions for which a singularity can occur for the time derivative of one of the field components. The resulting degenerate behavior can give rise to a shock wave with a reduction of the local number of degrees of freedom. We use an example model to illustrate the occurrence of superluminal propagation for field values approaching the singularity.
- Nonlinear vacuum electrodynamics and spontaneous breaking of Lorentz symmetryPublication . Escobar, C. A.; Potting, RobertusWe study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebanski, we apply a Dirac constraint analysis and derive an effective Hamiltonian. 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 local minima in which the field strength acquires a nonzero vacuum expectation value, thereby breaking Lorentz invariance spontaneously. These possible vacua can be classified in four classes, depending on the way Lorentz symmetry is broken. We show that the small field fluctuations around these vacua involve modes for which the dynamics can develop degeneracies, resulting in shock-wave-like and/or superluminal motion. Finally, we study the physical applicability of these models, and show how the Lorentz breaking vacua might in principle be detected by coupling the model to a suitable external current, or to gravity.
- Covariant quantization of CPT-violating photonsPublication . Colladay, D.; McDonald, P.; Noordmans, J. P.; Potting, RobertusWe perform the covariant canonical quantization of the CPT - and Lorentz-symmetry-violating photon sector of the minimal Standard-Model Extension, which contains a general (timelike, lightlike, or spacelike) fixed background tensor k(AF)(u). Well-known stability issues, arising from complex-valued energy states, are solved by introducing a small photon mass, orders of magnitude below current experimental bounds. We explicitly construct a covariant basis of polarization vectors, in which the photon field can be expanded. We proceed to derive the Feynman propagator and show that the theory is microcausal. Despite the occurrence of negative energies and vacuum-Cherenkov radiation, we do not find any runaway stability issues, because the energy remains bounded from below. An important observation is that the ordering of the roots of the dispersion relations is the same in any observer frame, which allows for a frame-independent condition that selects the correct branch of the dispersion relation. This turns out to be critical for the consistency of the quantization. To our knowledge, this is the first system for which quantization has consistently been performed, in spite of the fact that the theory contains negative energies in some observer frames.