标题： 修正的麦克斯韦电动力学的微扰量子化 显示英文标题

标题： Perturbative Quantization of Modified Maxwell Electrodynamics

摘要： 修正的麦克斯韦电动力学，简称ModMax，是唯一保留麦克斯韦理论显著对称性的非线性扩展：保形不变性和电磁对偶性。 尽管ModMax在经典层面上已经被广泛研究，但由于其非解析性质，在量子背景下几乎未被触及。 在这篇论文中，我们对该理论进行了微扰量子化。 利用背景场方法和维数正则化，通过计算单圈量子有效作用量，我们得到了新的修正项。 这些修正项在恒定场强的背景下消失，并且对于一般的背景场，它们并不具有经典理论的形式。 受到为ModMax获得的修正项的启发，我们将用于量化ModMax的方法应用于其二维类比理论。 同样地，通过计算所有一阶费曼图，我们在一般背景下得到了该理论的一阶量子有效作用量。 此外，我们研究了两类顶点图的无限级数的发散性。 显示英文摘要

摘要： Modified Maxwell electrodynamics, or ModMax for short, is the unique nonlinear extension of Maxwell's theory that preserves its notable symmetries: conformal invariance and electromagnetic duality. ModMax has been studied extensively at the classical level, however remains largely untouched in a quantum context due to its non-analytic nature. In this thesis, we perform the perturbative quantization of this theory. Using the background field method and dimensional regularization, we obtain novel corrections by calculating the one loop quantum effective action. These corrections vanish in a background with constant field strength, and are not of the form of the classical theory for a general background field. Motivated by the corrections obtained for ModMax, we applied the method developed to quantize ModMax to its two dimensional analogue theory. We similarly obtain the one loop quantum effective action for this theory in a general background by evaluating all one loop Feynman diagrams. In addition, we study the divergence of the separate infinite series of two vertex diagrams.