--- res: bibo_abstract: - After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Élliott foaf_name: Lieb, Élliott H foaf_surname: Lieb - foaf_Person: foaf_givenName: Robert foaf_name: Robert Seiringer foaf_surname: Seiringer foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6781-0521 - foaf_Person: foaf_givenName: Jakob foaf_name: Yngvason, Jakob foaf_surname: Yngvason bibo_doi: 10.1016/S0034-4877(07)80074-7 bibo_issue: '3' bibo_volume: 59 dct_date: 2007^xs_gYear dct_publisher: Elsevier@ dct_title: Bose-Einstein condensation and spontaneous symmetry breaking@ ...