{"paper":{"title":"(Pre-)Hilbert spaces in twistor quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Jun-ichi Note, Shinichi Deguchi","submitted_at":"2012-10-01T11:10:41Z","abstract_excerpt":"In twistor theory, the canonical quantization procedure, called twistor quantization, is performed with the twistor operators represented as \\hat{Z}^{A}=Z^{A}(\\in C) and \\hat{\\bar{Z}}_{A}=-\\frac{\\partial}{\\partial Z^{A}}. However, it has not been clarified what kind of function spaces this representation is valid in. In the present paper, we try to find appropriate (pre-)Hilbert spaces in which the above representation is realized as an adjoint pair of operators. To this end, we define an inner product for the helicity eigenfunctions by an integral over the product space of the circular space "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0349","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"}