{"paper":{"title":"Some properties of zero-mode wave functions in abelian Chern-Simons theory on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Yasuhiro Abe","submitted_at":"2017-11-20T02:16:42Z","abstract_excerpt":"In geometric quantization a zero-mode wave function in abelian Chern-Simons theory on the torus can be defined as $\\Psi [ a, \\bar{a} ] = e^{- \\frac{K(a, \\bar{a})}{2}} f (a)$ where $K(a ,\\bar{a} )$ denotes a K\\\"ahler potential for the zero-mode variable $a \\in \\mathbb{C}$ on the torus. We first review that the holomorphic wave function $f(a)$ can be described in terms of the Jacobi theta functions by imposing gauge invariance on $\\Psi [ a, \\bar{a} ]$ where gauge transformations are induced by doubly periodic translations of $a$. We discuss that $f(a)$ is quantum theoretically characterized by ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07122","kind":"arxiv","version":3},"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"}