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Rajagopal (Naval Research Laboratory, Brazil), Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, USA), Washington DC","submitted_at":"1999-03-05T20:59:23Z","abstract_excerpt":"The Lie-Trotter formula $e^{\\hat{A}+\\hat{B}} = \\lim_{N\\to \\infty} (e^{\\hat{A}/N} e^{\\hat{B}/N})^N$ is of great utility in a variety of quantum problems ranging from the theory of path integrals and Monte Carlo methods in theoretical chemistry, to many-body and thermostatistical calculations. We generalize it for the q-exponential function $e_q (x) = [1+ (1-q) x]^{(1/(1-q))}$ (with $e_1(x)=e^x$), and prove $e_q(\\hat{A}+\\hat{B}+(1-q) [\\hat{A}\\hat{B}+\\hat{B}\\hat{A}] /2) = \\lim_{N\\to \\infty} {[e_{1-(1-q)N}(\\hat{A}/N)] [e_{1-(1-q)N}(\\hat{B}/N)]}^N$. This extended formula is expected to be similarly"},"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":"cond-mat/9903106","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-03-05T20:59:23Z","cross_cats_sorted":[],"title_canon_sha256":"f912e2986cea9daa02339a0cd6fd4f61a81b648c63e9c446750d94f6eb3afae3","abstract_canon_sha256":"891c21484db503ce32f45b3103fba5babe816a78223c7071f0659f11ba8ec423"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:12:21.244401Z","signature_b64":"sXilhYLhkSRF2x5NMwGxC9MQWJ0B2rdrC2Fy4LeZEtGczAGyxmJQCpuCNjpEzLmv0jFg6PS56ZLgnhuXivoNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bde7c137a548f5bab5e54ddc934121e32178b58870c232324608b2a38ce7e270","last_reissued_at":"2026-07-04T16:12:21.244038Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:12:21.244038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalization of the Lie-Trotter Product Formula for q-Exponential Operators","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A.K. Rajagopal (Naval Research Laboratory, Brazil), Constantino Tsallis (Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ, USA), Washington DC","submitted_at":"1999-03-05T20:59:23Z","abstract_excerpt":"The Lie-Trotter formula $e^{\\hat{A}+\\hat{B}} = \\lim_{N\\to \\infty} (e^{\\hat{A}/N} e^{\\hat{B}/N})^N$ is of great utility in a variety of quantum problems ranging from the theory of path integrals and Monte Carlo methods in theoretical chemistry, to many-body and thermostatistical calculations. We generalize it for the q-exponential function $e_q (x) = [1+ (1-q) x]^{(1/(1-q))}$ (with $e_1(x)=e^x$), and prove $e_q(\\hat{A}+\\hat{B}+(1-q) [\\hat{A}\\hat{B}+\\hat{B}\\hat{A}] /2) = \\lim_{N\\to \\infty} {[e_{1-(1-q)N}(\\hat{A}/N)] [e_{1-(1-q)N}(\\hat{B}/N)]}^N$. 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