We study spontaneous breaking of Lorentz symmetry in nonlinear vacuum electrodynamics. Using a first-order formulation of the latter proposed by Plebański, 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.

中文翻译：

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非线性真空电动力学和洛伦兹对称性的自发破缺

我们研究非线性真空电动力学中洛伦兹对称性的自发破缺。使用 Plebański 提出的后者的一阶公式，我们应用狄拉克约束分析并推导出有效的哈密顿量。我们证明了存在一大类势能，其有效哈密顿量从下方有界，同时具有场强获得非零真空期望值的局部最小值，从而自发地打破洛伦兹不变性。这些可能的真空可以分为四类，这取决于洛伦兹对称性被破坏的方式。我们表明，这些真空周围的小场波动涉及动力学可以发展退化的模式，导致类似冲击波和/或超光速运动。最后，