Free electron gas in cavity quantum electrodynamics

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to photon are not available, both theory experiments rely mainly on finite-system models. Therefore paradigmatic example an exactly solvable system cavity becomes highly desireable. To fill gap we revisit Sommerfeld's free electron gas quantum electrodynamics (QED). We solve analytically long-wavelength limit arbitrary number non-interacting electrons, demonstrate that electron-photon ground state Fermi liquid which contains virtual photons. In contrast models finite systems, no exists if diamagentic $\textbf{A}^2$ term omitted. Further, performing linear response show induces plasmon-polariton excitations modifies optical DC conductivity gas. Our solution allows us consider thermodynamic electrons photons constructing effective theory. The continuum modes leads many-body renormalization mass, fermionic quasiparticle Wigner-Seitz radius interacting Lastly, how matter-modified repulsive Casimir force introduces dissipation into system. Several presented findings should be experimentally accessible.