Degenerate fermionic matter at N3LO: Quantum electrodynamics

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to -leading order (N3LO) 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 Oo alpha 3e ln alpha e thorn 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 N3LO calculation for cold and dense quark matter.

Automated summary

We have calculated the pressure of a cold and dense electron gas to a nearly complete N3LO in the fine-structure constant alpha e, using a new result for the two-loop photon self-energy. Our result includes all infrared-sensitive contributions to the pressure at this order, and only leaves a single undetermined coefficient associated with the contributions of unresummed hard momenta. We have also demonstrated the complete cancellation of infrared divergences according to the effective-field-theory paradigm by determining part of the hard contributions at this order.