{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:QJT65LUXJTS52WADLGU7ZDFNHT","short_pith_number":"pith:QJT65LUX","schema_version":"1.0","canonical_sha256":"8267eeae974ce5dd580359a9fc8cad3cc32d36e086104de5680ad69a8730848b","source":{"kind":"arxiv","id":"2107.06482","version":3},"attestation_state":"computed","paper":{"title":"Real-time dynamics of the $O(4)$ scalar theory within the fRG approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Wei-jie Fu, Yang-yang Tan, Yong-rui Chen","submitted_at":"2021-07-14T04:46:05Z","abstract_excerpt":"In this paper, the real-time dynamics of the $O(4)$ scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its $n$-point correlation functions are derived in terms of the \"classical\" and \"quantum\" fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the pha"},"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":"2107.06482","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2021-07-14T04:46:05Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"59e8669da955ef2cd9336da63b9f4c835a9a1bc24aa276593042c14538d8cb66","abstract_canon_sha256":"e00eb80deebbeb265212c1273cc2d7daa9ac6df94808879ba6d604f0e249817f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:14.852544Z","signature_b64":"FHNyxqKS3rSyxWSXmlmCzcxwmJBVJ4+mt5kqZm6i+ydlDY4S+7jk758ek+7iW+2OHT8vvmalljhOtOgprxmoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8267eeae974ce5dd580359a9fc8cad3cc32d36e086104de5680ad69a8730848b","last_reissued_at":"2026-07-05T03:49:14.852068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:14.852068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real-time dynamics of the $O(4)$ scalar theory within the fRG approach","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Wei-jie Fu, Yang-yang Tan, Yong-rui Chen","submitted_at":"2021-07-14T04:46:05Z","abstract_excerpt":"In this paper, the real-time dynamics of the $O(4)$ scalar theory is studied within the functional renormalization group formulated on the Schwinger-Keldysh closed time path. The flow equations for the effective action and its $n$-point correlation functions are derived in terms of the \"classical\" and \"quantum\" fields, and a concise diagrammatic representation is presented. An analytic expression for the flow of the four-point vertex is obtained. Spectral functions with different values of temperature and momentum are obtained. Moreover, we calculate the dynamical critical exponent for the pha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.06482","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.06482/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2107.06482","created_at":"2026-07-05T03:49:14.852130+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.06482v3","created_at":"2026-07-05T03:49:14.852130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.06482","created_at":"2026-07-05T03:49:14.852130+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJT65LUXJTS5","created_at":"2026-07-05T03:49:14.852130+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJT65LUXJTS52WAD","created_at":"2026-07-05T03:49:14.852130+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJT65LUX","created_at":"2026-07-05T03:49:14.852130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08505","citing_title":"Diffusion Models for Sampling Near Criticality in Lattice Field Theories","ref_index":68,"is_internal_anchor":true},{"citing_arxiv_id":"2606.03703","citing_title":"Phase structure of strong interaction matter from Functional QCD","ref_index":40,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT","json":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT.json","graph_json":"https://pith.science/api/pith-number/QJT65LUXJTS52WADLGU7ZDFNHT/graph.json","events_json":"https://pith.science/api/pith-number/QJT65LUXJTS52WADLGU7ZDFNHT/events.json","paper":"https://pith.science/paper/QJT65LUX"},"agent_actions":{"view_html":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT","download_json":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT.json","view_paper":"https://pith.science/paper/QJT65LUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.06482&json=true","fetch_graph":"https://pith.science/api/pith-number/QJT65LUXJTS52WADLGU7ZDFNHT/graph.json","fetch_events":"https://pith.science/api/pith-number/QJT65LUXJTS52WADLGU7ZDFNHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT/action/storage_attestation","attest_author":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT/action/author_attestation","sign_citation":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT/action/citation_signature","submit_replication":"https://pith.science/pith/QJT65LUXJTS52WADLGU7ZDFNHT/action/replication_record"}},"created_at":"2026-07-05T03:49:14.852130+00:00","updated_at":"2026-07-05T03:49:14.852130+00:00"}