Quantization and simulation of Born-Infeld non-linear electrodynamics on a lattice

TL;DR

This paper presents a lattice quantization of Born-Infeld non-linear electrodynamics, revealing quantum effects on electromagnetic fields and identifying a limiting conformal field theory at high non-linearity.

Contribution

The study introduces a lattice quantum formulation of Born-Infeld electrodynamics and analyzes its properties using Monte-Carlo simulations, extending classical analyses to the quantum regime.

Findings

D field matches Maxwell QED

E field is enhanced by quantum fluctuations

Quantum theory approaches a conformal field theory at high non-linearity

Abstract

Born-Infeld non-linear electrodynamics arises naturally as a field theory description of the dynamics of strings and branes. Most analyses of this theory have been limited to studying it as a classical field theory. We quantize this theory on a Euclidean 4-dimensional space-time lattice and determine its properties using Monte-Carlo simulations. The electromagnetic field around a static point charge is measured using Luscher-Weisz methods to overcome the sign problem associated with the introduction of this charge. The D field appears identical to that of Maxwell QED. However, the E field is enhanced by quantum fluctuations, while still showing the short distance screening observed in the classical theory. In addition, whereas for the classical theory, the screening increases without bound as the non-linearity increases, the quantum theory approaches a limiting conformal field theory.