{"paper":{"title":"Quantization of a Scalar Field in Two Poincar\\'e Patches of Anti-de Sitter Space and AdS/CFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ippei Fujisawa, Ryuichi Nakayama","submitted_at":"2014-03-10T09:52:22Z","abstract_excerpt":"Two sets of modes of a massive free scalar field are quantized in a pair of Poincar\\'e patches of Lorentzian anti-de Sitter (AdS) space, AdS$_{d+1}$ ($d \\geq 2$). It is shown that in Poincar\\'e coordinates $(r,t,\\vec{x})$, the two boundaries at $r=\\pm \\infty$ are connected. When the scalar mass $m$ satisfies a condition $0 < \\nu=\\sqrt{(d^2/4)+(m\\ell)^2} <1$, there exist two sets of mode solutions to Klein-Gordon equation, with distinct fall-off behaviors at the boundary. By using the fact that the boundaries at $r=\\pm \\infty$ are connected, a conserved Klein-Gordon norm can be defined for thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2200","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"}