{"paper":{"title":"Path integrals with discarded degrees of freedom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Luke M. Butcher","submitted_at":"2018-07-18T15:48:09Z","abstract_excerpt":"Whenever variables $\\phi=(\\phi^1,\\phi^2,\\ldots)$ are discarded from a system, and the discarded information capacity $\\mathcal{S}(x)$ depends on the value of an observable $x$, a quantum correction $\\Delta V_\\mathrm{eff}(x)$ appears in the effective potential [arXiv:1707.05789]. Here I examine the origins and implications of $\\Delta V_\\mathrm{eff}$ within the path integral, which I construct using Synge's world function. I show that the $\\phi$ variables can be `integrated out' of the path integral, reducing the propagator to a sum of integrals over observable paths $x(t)$ alone. The phase of e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07007","kind":"arxiv","version":2},"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"}