Perturbative Quantization of Modified Maxwell Electrodynamics

TL;DR

This paper performs the first perturbative quantization of ModMax electrodynamics, revealing quantum corrections that vanish in constant backgrounds and extending the method to a two-dimensional analogue.

Contribution

It introduces a novel perturbative quantization approach for ModMax electrodynamics and its 2D analogue, providing new insights into their quantum properties.

Findings

Quantum corrections vanish in constant field backgrounds

Derived the one-loop effective action for ModMax and its 2D analogue

Analyzed divergences in series of two-vertex diagrams

Abstract

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.