{"paper":{"title":"A Short Remark on the Polaron in the Semi-relativistic Pauli-Fierz Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Itaru Sasaki","submitted_at":"2013-03-30T00:26:29Z","abstract_excerpt":"We consider the polaron of the spinless semi-relativistic Pauli-Fierz model. The Hamiltonian of the model is defined by $H(\\mathbf{P}) = \\sqrt{(\\mathbf{P}-d\\Gamma(\\mathbf{k}) + e\\bA)^2 + M^2} + d\\Gamma(\\omega_m)$, where $\\mathbf{P}\\in\\mathbb{R}^3$ is the momentum of the polaron, $d\\Gamma(\\cdot)$ denotes the second quantization operator and $\\omega_m=|\\mathbf{k}|+m$ denotes the dispersion relation of the photon with virtual mass $m\\geq 0$. Let $E(\\mathbf{P})$ be the lowest energy of $H(\\mathbf{P})$. In this paper, we prove the inequality $E(\\mathbf{P} - \\mathbf{k}) - E(\\mathbf{P}) + \\omega_m(\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0051","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"}