{"paper":{"title":"Quantum fields in toroidal topology","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["gr-qc","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A.E. Santana, A.P.C. Malbouisson, F.C. Khanna, J.M.C. Malbouisson","submitted_at":"2011-07-28T13:38:45Z","abstract_excerpt":"The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ \\Gamma_{D}^{d}=(\\mathbb{S}^{1})^{d}\\times \\mathbb{M}^{D-d}$. The modular operator is generalized to introduce representations of isometry groups. The Poincar\\'{e} symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, that follows as a generalization of the Fourier-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5717","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"}