标题： 外部恒定背景对施加的库仑场的线性磁响应。 磁单极子解 显示英文标题

标题： Linear magnetic response of external constant backgrounds to an applied Coulomb field. Magnetic-monopole solution

摘要： 线性麦克斯韦方程，在红外近似下，研究了相对于恒定场背景的第一次幂偏差。 线性磁响应、由施加的静态有限尺寸电荷在任意组合的恒定和均匀电场和磁场中引起的线性电流和矢量势被讨论。 发现了两类解，即磁中性响应，其对应的磁荷为零，这是由于空间每一点都满足 Bianchi 恒等式的结果，以及磁荷响应，在后者中，该恒等式在原点$\mathbf{x}=0$处失效，从而导致非平凡的磁荷。 与磁中性响应相关的矢量势是无散度的，而对于后一种情况，发现它们是狄拉克弦，与无限多个点相关，这些点上的势是奇异的，并且局限于半轴。 所有与有效拉格朗日量及其导数成比例的系数都被专门用于量子电动力学，在其中详细讨论了强磁背景区域。 显示英文摘要

摘要： Linear Maxwell equations, corresponding to the first-power deviations from a constant-field background, are studied within the infrared approximation. Linear magnetic responses, linearly induced currents and vector potentials to an imposed static finite-sized charge in an arbitrary combination of constant and homogeneous electric and magnetic fields are discussed. Two class of solutions are found, namely, magnetically neutral responses whose corresponding magnetic charges are zero, as a result of the fulfillment of the Bianchi identity at every point of the space and a magnetically charged one, in which the latter identity fails at the origin $\mathbf{x}=0$, resulting to a nontrivial magnetic charge thereby. The vector potential associated with the magnetically neutral responses are free of divergence while, for the latter case, are found to be Dirac strings, associated with an infinite number of points, in which the potential is singular and restricted to half-axes. All coefficients, proportional to the effective lagrangian and derivatives of it, are specialized to Quantum Electrodynamics, wherein the strong magnetic background regime is discussed in detail.