{"paper":{"title":"Bose-Einstein condensation and Silver Blaze property from the two-loop $\\Phi$-derivable approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Gergely Mark\\'o, Urko Reinosa, Zsolt Sz\\'ep","submitted_at":"2014-10-26T08:11:01Z","abstract_excerpt":"We extend our previous investigation of the two-loop $\\Phi$-derivable approximation to finite chemical potential $\\mu$ and discuss Bose-Einstein condensation (BEC) in the case of a charged scalar field with $O(2)$ symmetry. We show that the approximation is renormalizable by means of counterterms which are independent of both the temperature and the chemical potential. We point out the presence of an additional skew contribution to the propagator as compared to the $\\mu=0$ case, which comes with its own gap equation (except at Hartree level). We solve this equation together with the field equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6998","kind":"arxiv","version":1},"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"}