{"paper":{"title":"Relation $Tr \\gamma_{5}= 0$ and the index theorem in lattice gauge theory","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-lat","authors_text":"Kazuo Fujikawa (Dept. of Physics, Univ. of Tokyo)","submitted_at":"1999-04-23T09:02:52Z","abstract_excerpt":"The relation $Tr \\gamma_{5}= 0$ implies the contribution to the trace from unphysical (would-be) species doublers in lattice gauge theory. This statement is also true for the Pauli-Villars regularization in continuum theory. If one insists on $Tr \\gamma_{5}= 0$, one thus inevitably includes unphysical states in the Hilbert space. If one truncates the trace to the contribution from physical species only, one obtains $\\tilde{T}r \\gamma_{5} = n_{+} - n_{-}$ which is equal to the Pontryagin index. A smooth continuum limit of $\\tilde{T}r \\gamma_{5} = Tr \\gamma_{5}(1-(a/2)D) = n_{+} - n_{-}$ for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9904007","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-lat/9904007/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}