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Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function $D(\\omega,{\\bf q})$ has the form $1/(gN(0))^2\\cdot (2\\Delta)^2/(\\omega^2-c_s^2{\\bf q}^2)$ with the coupling constant $g$ and $c_s=v_F/\\sqrt{3}$ for small $\\omega$ and ${\\bf q}$, with a pole at $\\omega=0$ "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.12444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.supr-con","submitted_at":"2019-03-29T10:49:48Z","cross_cats_sorted":[],"title_canon_sha256":"4134979c5222d3987229e9c8a325401b18e796bffc024444b2e44a225ecb27ee","abstract_canon_sha256":"780e923eada5082ac2b575baa4f321d063559d7e27164963eb953e7749fe2e47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:54.005339Z","signature_b64":"Q4zm/V/EE6JproLNw5VicDE+pj12O3RmFqcz+nzLGZCn7/eeu/9w75//es54PB53511sXkmCPg02rMRz9g2gCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"880178d9903984e6d2c3b0710b552ddb70df15759f21addf513dd965c8c3c639","last_reissued_at":"2026-05-17T23:49:54.004958Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:54.004958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Green's functions of Nambu-Goldstone modes and Higgs modes in superconductors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.supr-con","authors_text":"Takashi Yanagisawa","submitted_at":"2019-03-29T10:49:48Z","abstract_excerpt":"We examine fundamental properties of Green's functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function $D(\\omega,{\\bf q})$ has the form $1/(gN(0))^2\\cdot (2\\Delta)^2/(\\omega^2-c_s^2{\\bf q}^2)$ with the coupling constant $g$ and $c_s=v_F/\\sqrt{3}$ for small $\\omega$ and ${\\bf q}$, with a pole at $\\omega=0$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12444","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.12444","created_at":"2026-05-17T23:49:54.005014+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.12444v1","created_at":"2026-05-17T23:49:54.005014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12444","created_at":"2026-05-17T23:49:54.005014+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAAXRWMQHGCO","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAAXRWMQHGCONUWD","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAAXRWMQ","created_at":"2026-05-18T12:33:27.125529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N","json":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N.json","graph_json":"https://pith.science/api/pith-number/RAAXRWMQHGCONUWDWBYQWVJN3N/graph.json","events_json":"https://pith.science/api/pith-number/RAAXRWMQHGCONUWDWBYQWVJN3N/events.json","paper":"https://pith.science/paper/RAAXRWMQ"},"agent_actions":{"view_html":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N","download_json":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N.json","view_paper":"https://pith.science/paper/RAAXRWMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.12444&json=true","fetch_graph":"https://pith.science/api/pith-number/RAAXRWMQHGCONUWDWBYQWVJN3N/graph.json","fetch_events":"https://pith.science/api/pith-number/RAAXRWMQHGCONUWDWBYQWVJN3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N/action/storage_attestation","attest_author":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N/action/author_attestation","sign_citation":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N/action/citation_signature","submit_replication":"https://pith.science/pith/RAAXRWMQHGCONUWDWBYQWVJN3N/action/replication_record"}},"created_at":"2026-05-17T23:49:54.005014+00:00","updated_at":"2026-05-17T23:49:54.005014+00:00"}