{"paper":{"title":"Physicists' $d=3+1$, $N=1$ superspace-time and supersymmetric QFTs from a tower construction in complexified ${\\Bbb Z}/2$-graded $C^\\infty$-Algebraic Geometry and a purge-evaluation/index-contracting map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.SG"],"primary_cat":"hep-th","authors_text":"Chien-Hao Liu, Shing-Tung Yau","submitted_at":"2019-02-17T12:02:27Z","abstract_excerpt":"The complexified ${\\Bbb Z}/2$-graded $C^\\infty$-Algebraic Geometry aspect of a superspace(-time) $\\widehat{X}$ in Sec.\\,1 of D(14.1) (arXiv:1808.05011 [math.DG]) together with the Spin-Statistics Theorem in Quantum Field Theory, which requires fermionic components of a superfield be anticommuting, lead us to the notion of towered superspace(-time) $\\widehat{X}^{\\widehat{\\boxplus}}$ and the built-in purely even physics sector $X^{\\mbox{physics}}$ from $\\widehat{X}^{\\widehat{\\boxplus}}$. We use this to reproduce the $d=3+1$, $N=1$ Wess-Zumino model and the $d=3+1$, $N=1$ supersymmetric $U(1)$ ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.06246","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"}