Hedin equations in resonant micro-cavities

TL;DR

This paper generalizes the Hedin equations to include the dynamics of transverse photons, enabling accurate ab initio modeling of strongly coupled electron-photon systems like exciton-polaritons in micro-cavities.

Contribution

It introduces a novel theoretical framework extending Hedin equations to account for photon degrees of freedom in strongly coupled systems.

Findings

Derived generalized Hedin equations incorporating photon dynamics

Provides a foundation for ab initio calculations of light-matter interactions

Enables better understanding of exciton-polariton phenomena

Abstract

With the improvement of the experimental techniques, many new phenomena where the photon degrees of freedom are involved have been discovered. Typical examples are the exciton-polariton quasi-particles, excitons strongly coupled to photons. A correct description of these systems requires a full account of the photon's dynamics, including the vector gauge degrees of freedom. In order to include this contribution in \emph{ab initio} many-body perturbation theories, here we present a generalization of the Hedin equations, originally derived for a many electron system with Coulomb interaction. These equations are now derived in order to take into account the strong coupling physics of the electrons and the \textit{transverse} photon's degrees of freedom.