{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:K7YEQFBPF3PGOS5XU2GHIOTSRL","short_pith_number":"pith:K7YEQFBP","schema_version":"1.0","canonical_sha256":"57f048142f2ede674bb7a68c743a728aea1b335e3bcfa48288aadb0e20da6114","source":{"kind":"arxiv","id":"physics/9707010","version":1},"attestation_state":"computed","paper":{"title":"Immersion Anomaly of Dirac Operator on Surface in R^3","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shigeki Matsutani","submitted_at":"1997-07-10T11:16:00Z","abstract_excerpt":"In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in $R^3$ by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward-Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface."},"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":"physics/9707010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1997-07-10T11:16:00Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3428924e6716bc163a73e6a5677030fb2c148f94d74714c52bc8ba7324dee70e","abstract_canon_sha256":"8bc9a3dd649772259b9c85821eff40d99d4a09de54b125b99280d22d40616520"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:07.162649Z","signature_b64":"JFIhrJxKzY6uZ41o9t2haCqw3qmCR9SyWCAb9eFPMbUt6rosWDzWdJxkgGb/hoYS/AePG3IXFUTcrSLjBEgcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57f048142f2ede674bb7a68c743a728aea1b335e3bcfa48288aadb0e20da6114","last_reissued_at":"2026-05-18T02:35:07.162031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:07.162031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Immersion Anomaly of Dirac Operator on Surface in R^3","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shigeki Matsutani","submitted_at":"1997-07-10T11:16:00Z","abstract_excerpt":"In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in $R^3$ by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward-Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/9707010","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":"physics/9707010","created_at":"2026-05-18T02:35:07.162119+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/9707010v1","created_at":"2026-05-18T02:35:07.162119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/9707010","created_at":"2026-05-18T02:35:07.162119+00:00"},{"alias_kind":"pith_short_12","alias_value":"K7YEQFBPF3PG","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"K7YEQFBPF3PGOS5X","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"K7YEQFBP","created_at":"2026-05-18T12:25:48.327863+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/K7YEQFBPF3PGOS5XU2GHIOTSRL","json":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL.json","graph_json":"https://pith.science/api/pith-number/K7YEQFBPF3PGOS5XU2GHIOTSRL/graph.json","events_json":"https://pith.science/api/pith-number/K7YEQFBPF3PGOS5XU2GHIOTSRL/events.json","paper":"https://pith.science/paper/K7YEQFBP"},"agent_actions":{"view_html":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL","download_json":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL.json","view_paper":"https://pith.science/paper/K7YEQFBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/9707010&json=true","fetch_graph":"https://pith.science/api/pith-number/K7YEQFBPF3PGOS5XU2GHIOTSRL/graph.json","fetch_events":"https://pith.science/api/pith-number/K7YEQFBPF3PGOS5XU2GHIOTSRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL/action/storage_attestation","attest_author":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL/action/author_attestation","sign_citation":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL/action/citation_signature","submit_replication":"https://pith.science/pith/K7YEQFBPF3PGOS5XU2GHIOTSRL/action/replication_record"}},"created_at":"2026-05-18T02:35:07.162119+00:00","updated_at":"2026-05-18T02:35:07.162119+00:00"}