{"paper":{"title":"The dynamical sine-Gordon model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Hao Shen, Martin Hairer","submitted_at":"2014-09-19T16:55:55Z","abstract_excerpt":"We introduce the dynamical sine-Gordon equation in two space dimensions with parameter $\\beta$, which is the natural dynamic associated to the usual quantum sine-Gordon model. It is shown that when $\\beta^2 \\in (0,\\frac{16\\pi}{3})$ the Wick renormalised equation is well-posed. In the regime $\\beta^2 \\in (0,4\\pi)$, the Da Prato-Debussche method applies, while for $\\beta^2 \\in [4\\pi,\\frac{16\\pi}{3})$, the solution theory is provided via the theory of regularity structures (Hairer 2013). We also show that this model arises naturally from a class of $2+1$-dimensional equilibrium interface fluctuat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5724","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"}