{"paper":{"title":"An inverse scattering problem for the Klein-Gordon equation with a classical source in quantum field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Akito Suzuki, Hironobu Sasaki","submitted_at":"2011-01-01T00:03:17Z","abstract_excerpt":"An inverse scattering problem for a quantized scalar field ${\\bm \\phi}$ obeying a linear Klein-Gordon equation $(\\square + m^2 + V) {\\bm \\phi} = J \\mbox{in $\\mathbb{R} \\times \\mathbb{R}^3$}$ is considered, where $V$ is a repulsive external potential and $J$ an external source $J$. We prove that the scattering operator $\\mathscr{S}= \\mathscr{S}(V,J)$ associated with ${\\bm \\phi}$ uniquely determines $V$. Assuming that $J$ is of the form $J(t,x)=j(t)\\rho(x)$, $(t,x) \\in \\mathbb{R} \\times \\mathbb{R}^3$, we represent $\\rho$ (resp. $j$) in terms of $j$ (resp. $\\rho$) and $\\mathscr{S}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0310","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"}