{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:K2WZOTXGG3BE22WUKQPGT5Z3RZ","short_pith_number":"pith:K2WZOTXG","schema_version":"1.0","canonical_sha256":"56ad974ee636c24d6ad4541e69f73b8e6e5cea678c39c39f3c4defde4d590d4f","source":{"kind":"arxiv","id":"1104.3381","version":5},"attestation_state":"computed","paper":{"title":"Formulation of Complex Action Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Holger Bech Nielsen, Keiichi Nagao","submitted_at":"2011-04-18T04:58:34Z","abstract_excerpt":"We formulate a complex action theory which includes operators of coordinate and momentum $\\hat{q}$ and $\\hat{p}$ being replaced with non-hermitian operators $\\hat{q}_{new}$ and $\\hat{p}_{new}$, and their eigenstates ${}_m <_{new} q |$ and ${}_m <_{new} p |$ with complex eigenvalues $q$ and $p$. Introducing a philosophy of keeping the analyticity in path integration variables, we define a modified set of complex conjugate, real and imaginary parts, hermitian conjugates and bras, and explicitly construct $\\hat{q}_{new}$, $\\hat{p}_{new}$, ${}_m <_{new} q |$ and ${}_m <_{new} p |$ by formally sque"},"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":"1104.3381","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-04-18T04:58:34Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"41233d288938e806008067d7c9f215afa8b0a0dd529e5ebd5c5d852c75a585d9","abstract_canon_sha256":"eb85e1f82686441d3787416c26b2832d94d7f6f6965d434063a2d1e9e4f6033d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:25.272803Z","signature_b64":"IQap9+sspbRWFxN9Qb7Zq9d78oZQKAkAgoxiuxPUiT8OnbBtXBoznHa2fzgP2TyT8hEuFDa9ceBoOrO756c2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56ad974ee636c24d6ad4541e69f73b8e6e5cea678c39c39f3c4defde4d590d4f","last_reissued_at":"2026-05-18T03:57:25.271889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:25.271889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Formulation of Complex Action Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Holger Bech Nielsen, Keiichi Nagao","submitted_at":"2011-04-18T04:58:34Z","abstract_excerpt":"We formulate a complex action theory which includes operators of coordinate and momentum $\\hat{q}$ and $\\hat{p}$ being replaced with non-hermitian operators $\\hat{q}_{new}$ and $\\hat{p}_{new}$, and their eigenstates ${}_m <_{new} q |$ and ${}_m <_{new} p |$ with complex eigenvalues $q$ and $p$. Introducing a philosophy of keeping the analyticity in path integration variables, we define a modified set of complex conjugate, real and imaginary parts, hermitian conjugates and bras, and explicitly construct $\\hat{q}_{new}$, $\\hat{p}_{new}$, ${}_m <_{new} q |$ and ${}_m <_{new} p |$ by formally sque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3381","kind":"arxiv","version":5},"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":"1104.3381","created_at":"2026-05-18T03:57:25.272041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3381v5","created_at":"2026-05-18T03:57:25.272041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3381","created_at":"2026-05-18T03:57:25.272041+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2WZOTXGG3BE","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2WZOTXGG3BE22WU","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2WZOTXG","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.06716","citing_title":"Approximate Minimal SU(5), Several Fundamental Scales, Fluctuating Lattice","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ","json":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ.json","graph_json":"https://pith.science/api/pith-number/K2WZOTXGG3BE22WUKQPGT5Z3RZ/graph.json","events_json":"https://pith.science/api/pith-number/K2WZOTXGG3BE22WUKQPGT5Z3RZ/events.json","paper":"https://pith.science/paper/K2WZOTXG"},"agent_actions":{"view_html":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ","download_json":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ.json","view_paper":"https://pith.science/paper/K2WZOTXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3381&json=true","fetch_graph":"https://pith.science/api/pith-number/K2WZOTXGG3BE22WUKQPGT5Z3RZ/graph.json","fetch_events":"https://pith.science/api/pith-number/K2WZOTXGG3BE22WUKQPGT5Z3RZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ/action/storage_attestation","attest_author":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ/action/author_attestation","sign_citation":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ/action/citation_signature","submit_replication":"https://pith.science/pith/K2WZOTXGG3BE22WUKQPGT5Z3RZ/action/replication_record"}},"created_at":"2026-05-18T03:57:25.272041+00:00","updated_at":"2026-05-18T03:57:25.272041+00:00"}