{"paper":{"title":"The on-shell self-energy of the uniform electron gas in its weak-correlation limit","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Paul Ziesche","submitted_at":"2006-09-07T11:07:50Z","abstract_excerpt":"The ring-diagram partial summation (or RPA) for the ground-state energy of the uniform electron gas (with the density parameter $r_s$) in its weak-correlation limit $r_s\\to 0 $ is revisited. It is studied, which treatment of the self-energy $\\Sigma(k,\\omega)$ is in agreement with the Hugenholtz-van Hove (Luttinger-Ward) theorem $\\mu-\\mu_0= \\Sigma(k_{\\rm F},\\mu)$ and which is not. The correlation part of the lhs h as the RPA asymptotics $a\\ln r_s +a'+O(r_s)$ [in atomic units]. The use of renormalized RPA diagrams for the rhs yields the similar expression $a\\ln r_s+a''+O(r_s)$ with the sum rule "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609168","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}