{"paper":{"title":"Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.quant-gas","authors_text":"Daisuke A. Takahashi, Muneto Nitta","submitted_at":"2014-04-30T12:19:08Z","abstract_excerpt":"When continuous symmetry is spontaneously broken, there appear Nambu-Goldstone modes (NGMs) with linear and quadratic dispersion relations, which are called type-I and type-II, respectively. We propose a framework to count these modes including the coefficients of the dispersion relations with applying the standard Gross-Pitaevskii-Bogoliubov theory. Our method is mainly based on (i) zero-mode solutions of the Bogoliubov equation originated from spontaneous symmetry breaking and (ii) their generalized orthogonal relations, which naturally arises from well-known Bogoliubov transformations and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7696","kind":"arxiv","version":3},"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"}