{"paper":{"title":"The Shape of Compact Toroidal Dimensions $T^d_{\\theta}$ and the Casimir Effect on $M^D\\times T^d_{\\theta}$ spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"V.K.Oikonomou","submitted_at":"2009-05-29T17:50:45Z","abstract_excerpt":"We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is $M^D\\times T^2_{\\theta}$, where $M^D$ is the $D$ dimensional Minkowski spacetime and $T^2_{\\theta}$ the twisted torus described by $R_1$, $R_2$ and $\\theta$. For the case $R_1=R_2$ we found that the massive bulk scalar field Casimir energy is singular for $D$=even and this singularity is $R$-dependent and remains even when the force is calculated. Also the massless Casimir energy and force"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4928","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"}