{"paper":{"title":"Binding condition for a general class of quantum field Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Christian G\\'erard, Itaru Sasaki","submitted_at":"2012-06-21T02:56:33Z","abstract_excerpt":"We consider a system of a quantum particle interacting with a quantum field and an external potential $V(\\bx)$. The Hamiltonian is defined by a quadratic form $H^V = H^0 + V(\\bx)$, where $H^0$ is a quadratic form which preserves the total momentum. $H^0$ and $H^V$ are assumed to be bounded from below. We give a criterion for the positivity of the binding energy $E_\\mathrm{bin} = E^0-E^V$, where $E^0$ and $E^V$ are the ground state energies of $H^0$ and $H^V$. As examples of the result, the positivity of the binding energy of the semi-relativistic Pauli-Fierz model and Nelson type Hamiltonian i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4764","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"}