一个受 Dirac 材料启发的非线性电动力学模型
A Dirac-material-inspired non-linear electrodynamic model
AI总结：
本文提出一种受 Dirac 材料启发的非线性电动力学模型，推广单圈有效 Lagrangian，并证明其具有真空双折射及磁场相关的类 Coulomb 屏蔽势。
摘要：
我们提出并研究了一种受 Dirac 材料物理学启发而产生的非线性电动力学的性质。这一新的电动力学模型是对文献 [3] 中所计算的单圈修正非线性有效 Lagrangian 的推广。在强磁场和弱电场的特定情形下，它退化为文献 [3] 作者所建立的光子非线性模型。我们通过分析介电常数张量和磁导率张量的性质、能量-动量张量以及在均匀磁场背景存在时的波传播效应，继续研究所提出的模型。结果表明，这里给出的电动力学表现出真空双折射现象。随后，我们仍在均匀外磁场存在的情况下，计算了对相互作用能的最低阶修正。我们的分析是在规范不变但依赖路径的变量形式体系框架内进行的。计算揭示出一种屏蔽的类 Coulomb 势，其具有随外磁场跑动的有效电荷；但是，正如对 Dirac 型材料所预期的那样，每当外磁场被关闭时，这种屏蔽就会消失。
英文摘要：
We propose and study the properties of a non-linear electrodynamics that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in the work of ref. [3]. In the particular regime of a strong magnetic and a weak electric field, it reduces to the photonic non-linear model worked out by the authors of ref. [3]. We pursue our investigation of the proposed model by analyzing properties of the permittivity and permeability tensors, the energy-momentum tensor and wave propagation effects in presence of a uniform magnetic background. It is shown that the electrodynamics here presented exhibits the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy, considering still the presence of a uniform external magnetic field. Our analysis is carried out within the framework of the gauge-invariant but path-dependent variables formalism. The calculation reveals a screened Coulomb-like potential with an effective electric charge that runs with the external magnetic field but, as expected for Dirac-type materials, the screening disappears whenever the external magnetic field is switched off.
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