--- _id: '2359' abstract: - lang: eng text: The validity of substituting a c-number z for the k = 0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive. author: - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Lieb É, Seiringer R, Yngvason J. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 2005;94(8). doi:10.1103/PhysRevLett.94.080401 apa: Lieb, É., Seiringer, R., & Yngvason, J. (2005). Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.94.080401 chicago: Lieb, Élliott, Robert Seiringer, and Jakob Yngvason. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters. American Physical Society, 2005. https://doi.org/10.1103/PhysRevLett.94.080401. ieee: É. Lieb, R. Seiringer, and J. Yngvason, “Justification of c-number substitutions in bosonic hamiltonians,” Physical Review Letters, vol. 94, no. 8. American Physical Society, 2005. ista: Lieb É, Seiringer R, Yngvason J. 2005. Justification of c-number substitutions in bosonic hamiltonians. Physical Review Letters. 94(8). mla: Lieb, Élliott, et al. “Justification of C-Number Substitutions in Bosonic Hamiltonians.” Physical Review Letters, vol. 94, no. 8, American Physical Society, 2005, doi:10.1103/PhysRevLett.94.080401. short: É. Lieb, R. Seiringer, J. Yngvason, Physical Review Letters 94 (2005). date_created: 2018-12-11T11:57:12Z date_published: 2005-03-04T00:00:00Z date_updated: 2021-01-12T06:57:00Z day: '04' doi: 10.1103/PhysRevLett.94.080401 extern: 1 intvolume: ' 94' issue: '8' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0412023 month: '03' oa: 1 publication: Physical Review Letters publication_status: published publisher: American Physical Society publist_id: '4566' quality_controlled: 0 status: public title: Justification of c-number substitutions in bosonic hamiltonians type: journal_article volume: 94 year: '2005' ...