{"arxiv_id":"hep-ph/0412245","title":"Simple derivation of general Fierz-type identities","abstract":"General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex $4\\times4$ matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning.","primary_cat":"hep-ph","cross_cats":["hep-th","physics.ed-ph"],"submitted_at":"2004-12-17T07:29:45+00:00","latest_version":4,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":"ACCEPT","confidence":"HIGH","one_line_summary":"Fierz-type identities are recast as completeness relations in matrix vector spaces, and a chiral basis yields the chiral Fierz identities systematically.","novelty_score":4.0,"correctness_risk":"low","formal_verification":"none","upvotes":0,"downvotes":0,"pith_score":0,"inbound_count":16,"_links":{"html":"https://pith.science/paper/hep-ph/0412245","verdict":"/api/v1/verdicts/hep-ph/0412245"}}