{"paper":{"title":"The $\\partial$-complex on the Fock space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Friedrich Haslinger","submitted_at":"2018-05-11T09:39:12Z","abstract_excerpt":"We study certain densely defined unbounded operators on the Fock space. These are the annihilation and creation operators of quantum mechanics. In several complex variables we have the $\\partial$-operator and its adjoint $\\partial^*$ acting on $(p,0)$-forms with coefficients in the Fock space. We consider the corresponding $\\partial$-complex and study spectral properties of the corresponding complex Laplacian $\\tilde \\Box = \\partial \\partial^* + \\partial^*\\partial.$ Finally we study a more general complex Laplacian $\\tilde \\Box_D = D D^* + D^* D,$ where $D$ is a differential operator of polyno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04293","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"}