Polarization effects in modified versions of the QED vacuum

探索量子真空对于获得对自然基本规律的深入而清晰的理解至关重要。经典真空只是描述了一个没有物质的区域，而量子电动力学揭示了它的特征是带电量子场的波动。这使得量子真空可以被理解为“虚拟”电子-正电子对的等离子体，它的行为就像一个弱非线性的介电介质。因此，外场可以使真空极化，改变其介电特性并诱导大量色散和吸收现象。其中一些，如著名的原子能级的兰姆位移，已经得到了证实，并且可以在实验中以很高的精度进行测量。其他现象，如真空双折射和真空中自发产生的真正的电子-正电子对，到目前为止还没有被观察到，尽管人们在实验探测方面做了很大的努力。这是由于在达到以电子质量为特征的临界尺度附近的场强方面的技术限制。在这个理论项目中，我们计划研究类似于电子-正电子量子真空的真空场景，其现象学的特征是更低的能量和场尺度。这种量子真空出现在物理学的各个领域。它们的范围从特殊的凝聚态物质系统（石墨烯），其中价带中的电子表现得像低质量的粒子，到粒子物理学的高级理论，预测了非常轻的、弱相互作用的粒子（如轴子和微电荷）的存在。所考虑的情形可分为三类：(a)低维系统的量子真空；(b)涉及假想光粒子波动的量子真空；(c)外场存在下的量子真空。相应的极化效应发生在能量尺度上，可以用目前可用的高精度技术（如原子光谱、极化法和电压计量）进行实验探测。我们的目标是双重的。(1)我们希望利用实验验证的真空极化效应，如兰姆位移和光子分裂，来探测新的候选粒子。从这些实验以及在类似卡文迪许的装置中获得的灵敏度，将推断出类轴子粒子和微小电荷的参数空间的严格界限。(2)对于迄今未观察到的效应（如真空双折射或真空衰减成对），我们将研究具有密切相关性质的系统中的类比，并探索扩大这些效应的新方法。广泛的技术，包括维度紧化，重整化，量子动力学方程和微扰理论。我们的研究将揭示不同类别的量子真空之间的相互关系，并显著推进我们对各种尚未观察到的真空极化现象的理解。

Exploring the quantum vacuum is central to obtain an in-depth and clear understanding of the fundamental laws of nature. While the classical vacuum simply describes a region devoid of matter, quantum electrodynamics reveals that it is characterized by fluctuations of charged quantum fields. This allows the quantum vacuum to be understood as a plasma of "virtual" electron-positron pairs, which behaves like a weakly nonlinear, dielectric medium. An external field can thus polarize the vacuum, altering its dielectric properties and inducing a multitude of dispersive and absorptive phenomena. Some of them, like the famous Lamb shift of atomic energy levels, are well-established and can be measured with high accuracy in experiment. Others, like vacuum birefringence and the spontaneous production of real electron-positron pairs from the vacuum, have so far eluded observation - in spite of strong efforts towards their experimental detections. This is due to the technical limitations of reaching field strengths near the critical scale characterized by the electron mass.In this theoretical project, we plan to study vacuum scenarios resembling the electron-positron quantum vacuum, whose phenomenologies are characterized by much lower energy and field scales. Quantum vacua of this kind arise in various areas of physics. They range from special condensed-matter systems (graphene) where the electrons in the valence band behave like low-mass particles, to advanced theories of particle physics which predict the existence of very light, weakly interacting particles (such as axions and minicharges). The scenarios to be considered can be classified in three categories: (a) quantum vacua of low-dimensional systems; (b) quantum vacua involving fluctuations of hypothetical light particles; (c) quantum vacua in the presence of external fields. The corresponding polarization effects occur on energy scales that can be probed experimentally with currently available high-precision techniques such as atomic spectroscopy, polarimetry and voltage metering.Our aims are twofold. (1) We want to make use of experimentally verified vacuum polarization effects, such as the Lamb shift and photon splitting, to probe new particle candidates. From the sensitivities achieved in these experiments as well as in Cavendish-like setups, stringent bounds on the parameter spaces of axion-like particles and minicharges will be infered. (2) With regard to hitherto unobserved effects (such as vacuum birefringence or vacuum decay into pairs), we shall study analogies in systems with closely related properties, and explore novel ways to amplify these effects. A broad range of techniques shall be used, including dimensional compactification, renormalization, quantum kinetic equations and perturbation theory. Our studies will reveal interrelations between different classes of the quantum vacuum and significantly advance our understanding of various yet unobserved vacuum polarization phenomena.