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Complete four-loop pressure of cold QED
Abstract
Extending the weak-coupling expansion of the pressure of a cold and dense ultrarelativistic electron gas to next-to-next-to-next-to-leading order (N3LO) in the gauge coupling has remained an open problem since the classic N2LO result of Freedman and McLerran, published in 1977. Here, we present the full N3LO pressure, the first thermodynamic quantity determined to this order in a physical gauge theory. The pressure exhibits good perturbative convergence and weak renormalization-scale dependence even at sizable couplings, while a Bayesian analysis of missing higher-order contributions indicates uncertainties that can exceed those inferred from scale variation alone.
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BibTeX
@misc{karkkainen2026complete,
title = {{Complete four-loop pressure of cold QED}},
author = {Aapeli Kärkkäinen and Pablo Navarrete and Mika Nurmela and Kaapo Seppänen and Samuel Abreu and Maximilian Delto and Aleksi Kurkela and Risto Paatelainen and Aleksi Vuorinen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13873},
eprint = {2610.13873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13873},
}
RIS
TY - UNPB
TI - Complete four-loop pressure of cold QED
AU - Aapeli Kärkkäinen
AU - Pablo Navarrete
AU - Mika Nurmela
AU - Kaapo Seppänen
AU - Samuel Abreu
AU - Maximilian Delto
AU - Aleksi Kurkela
AU - Risto Paatelainen
AU - Aleksi Vuorinen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13873
UR - https://arxiv.org/abs/2610.13873
AB - Extending the weak-coupling expansion of the pressure of a cold and dense ultrarelativistic electron gas to next-to-next-to-next-to-leading order (N3LO) in the gauge coupling has remained an open problem since the classic N2LO result of Freedman and McLerran, published in 1977. Here, we present the full N3LO pressure, the first thermodynamic quantity determined to this order in a physical gauge theory. The pressure exhibits good perturbative convergence and weak renormalization-scale dependence even at sizable couplings, while a Bayesian analysis of missing higher-order contributions indicates uncertainties that can exceed those inferred from scale variation alone.
ER -