{"paper":{"title":"Multi-Time Wave Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Matthias Lienert, Roderich Tumulka, S\\\"oren Petrat","submitted_at":"2017-02-17T09:54:20Z","abstract_excerpt":"In non-relativistic quantum mechanics of $N$ particles in three spatial dimensions, the wave function $\\psi(q_1,\\ldots,q_N,t)$ is a function of $3N$ position coordinates and one time coordinate. It is an obvious idea that in a relativistic setting, such functions should be replaced by $\\phi((t_1,q_1),\\ldots,(t_N,q_N))$, a function of $N$ space-time points called a multi-time wave function because it involves $N$ time variables. Its evolution is determined by $N$ Schr\\\"odinger equations, one for each time variable; to ensure that simultaneous solutions to these $N$ equations exist, the $N$ Hami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05282","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"}