{"paper":{"title":"Spectral and scattering theory of charged $P(\\varphi)_2$ models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christian G\\'erard (LM-Orsay)","submitted_at":"2009-06-30T11:11:47Z","abstract_excerpt":"We consider in this paper space-cutoff charged $P(\\varphi)_{2}$ models arising from the quantization of the non-linear charged Klein-Gordon equation: \\[ (\\p_{t}+\\i V(x))^{2}\\phi(t, x)+ (-\\Delta_{x}+ m^{2})\\phi(t,x)+ g(x)\\p_{\\overline{z}}P(\\phi(t,x), \\overline{\\phi}(t,x))=0, \\] where $V(x)$ is an electrostatic potential, $g(x)\\geq 0$ a space-cutoff and $P(\\lambda, \\overline{\\lambda})$ a real bounded below polynomial. We discuss various ways to quantize this equation, starting from different CCR representations. After describing the construction of the interacting Hamiltonian $H$ we study its sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5478","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"}