{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:YGL6ZTDQFSCEVVYBPF5CKSFJYO","short_pith_number":"pith:YGL6ZTDQ","schema_version":"1.0","canonical_sha256":"c197eccc702c844ad701797a2548a9c39737ee837fc61d3ab71098b4c12eef54","source":{"kind":"arxiv","id":"1008.1776","version":1},"attestation_state":"computed","paper":{"title":"On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Thomas-Paul Hack","submitted_at":"2010-08-10T19:21:24Z","abstract_excerpt":"First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of the Hadamard coefficients of the Dirac field, it is found that a construction of a stress-energy tensor"},"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":"1008.1776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-08-10T19:21:24Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"f8c9afe348b124564283a2dc005f3bf6e619a7acef3fb0fa79e6d7c11827f53d","abstract_canon_sha256":"6b338f18415bc1ab7f8cb00daddc1fa761a28de0e700b6df3f7c6ce70d7d91a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:59.053901Z","signature_b64":"wPJZsWtw/nZsv+DQeLSCwbeDu7BDb5MuICxSpeFnMHEZnWsGRGukHuglLLOYpuq/yvRtyni2NeQvK4lfrNmYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c197eccc702c844ad701797a2548a9c39737ee837fc61d3ab71098b4c12eef54","last_reissued_at":"2026-05-18T04:38:59.053112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:59.053112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Backreaction of Scalar and Spinor Quantum Fields in Curved Spacetimes - From the Basic Foundations to Cosmological Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Thomas-Paul Hack","submitted_at":"2010-08-10T19:21:24Z","abstract_excerpt":"First, the present work is concerned with generalising constructions and results in quantum field theory on curved spacetimes from the well-known case of the Klein-Gordon field to Dirac fields. To this end, the enlarged algebra of observables of the Dirac field is constructed in the algebraic framework. This algebra contains normal-ordered Wick polynomials in particular, and an extended analysis of one of its elements, the stress-energy tensor, is performed. Based on detailed calculations of the Hadamard coefficients of the Dirac field, it is found that a construction of a stress-energy tensor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1776","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":"1008.1776","created_at":"2026-05-18T04:38:59.053252+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.1776v1","created_at":"2026-05-18T04:38:59.053252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1776","created_at":"2026-05-18T04:38:59.053252+00:00"},{"alias_kind":"pith_short_12","alias_value":"YGL6ZTDQFSCE","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"YGL6ZTDQFSCEVVYB","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"YGL6ZTDQ","created_at":"2026-05-18T12:26:17.028572+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/YGL6ZTDQFSCEVVYBPF5CKSFJYO","json":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO.json","graph_json":"https://pith.science/api/pith-number/YGL6ZTDQFSCEVVYBPF5CKSFJYO/graph.json","events_json":"https://pith.science/api/pith-number/YGL6ZTDQFSCEVVYBPF5CKSFJYO/events.json","paper":"https://pith.science/paper/YGL6ZTDQ"},"agent_actions":{"view_html":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO","download_json":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO.json","view_paper":"https://pith.science/paper/YGL6ZTDQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.1776&json=true","fetch_graph":"https://pith.science/api/pith-number/YGL6ZTDQFSCEVVYBPF5CKSFJYO/graph.json","fetch_events":"https://pith.science/api/pith-number/YGL6ZTDQFSCEVVYBPF5CKSFJYO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO/action/storage_attestation","attest_author":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO/action/author_attestation","sign_citation":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO/action/citation_signature","submit_replication":"https://pith.science/pith/YGL6ZTDQFSCEVVYBPF5CKSFJYO/action/replication_record"}},"created_at":"2026-05-18T04:38:59.053252+00:00","updated_at":"2026-05-18T04:38:59.053252+00:00"}