An Open Effective Field Theory for light in a medium

TL;DR

This paper develops a comprehensive open effective field theory for electromagnetism in media, incorporating dissipative effects and gauge invariance, with implications for understanding open quantum systems and gravity.

Contribution

It constructs the most general open EFT for electromagnetism, revealing how gauge symmetry is deformed by dissipation and establishing gauge-invariant photon propagators with noise constraints.

Findings

Gauge symmetry is deformed by dissipative effects.

Photon propagators are gauge-invariant.

Noise fluctuations are constrained by gauge invariance.

Abstract

In many scenarios of interest, a quantum system interacts with an unknown environment, necessitating the use of open quantum system methods to capture dissipative effects and environmental noise. With the long-term goal of developing a perturbative theory for open quantum gravity, we take an important step by studying Abelian gauge theories within the Schwinger-Keldysh formalism. We begin with a pedagogical review of general results for open free theories, setting the stage for our primary focus: constructing the most general open effective field theory for electromagnetism in a medium. We assume locality in time and space, but allow for an arbitrary finite number of derivatives. Crucially, we demonstrate that the two copies of the gauge group associated with the two branches of the Schwinger-Keldysh contour are not broken but are instead deformed by dissipative effects. We provide a thorough discussion of gauge fixing, define covariant gauges, and calculate the photon propagators, proving that they yield gauge-invariant results. A notable result is the discovery that gauge invariance is accompanied by non-trivial constraints on noise fluctuations. We derive these constraints through three independent methods, highlighting their fundamental significance for the consistent formulation of open quantum gauge theories.