{"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 $e_q(\\hat{A}+\\hat{B}+(1-q) [\\hat{A}\\hat{B}+\\hat{B}\\hat{A}] /2) = \\lim_{N\\to \\infty} {[e_{1-(1-q)N}(\\hat{A}/N)] [e_{1-(1-q)N}(\\hat{B}/N)]}^N$. This extended formula is expected to be similarly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9903106","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/9903106/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"}