Degenerate fermionic matter at N$^3$LO: Quantum Electrodynamics

TL;DR

This paper calculates the pressure of a cold, dense electron gas at N$^3$LO in QED, including all infrared-sensitive contributions, marking a significant advancement in precision for quantum many-body systems.

Contribution

It provides the first comprehensive N$^3$LO calculation of the electron gas pressure, incorporating a new two-loop photon self-energy result and demonstrating infrared divergence cancellation.

Findings

Complete N$^3$LO pressure expression for electron gas

Inclusion of all infrared-sensitive contributions

Demonstration of divergence cancellation

Abstract

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N$^3$LO) in the fine-structure constant $\alpha_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O(\alpha_e^3 \ln \alpha_e^{ })$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N$^3$LO calculation for cold and dense quark matter.