2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152743The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually local fields is proved and consequently a direct proof of Li's theorem on a local system of vertex operators is provided. Several characterizations of vertex algebras are also discussed.43 pages, no figures, Latex2e files using amsmath,amssymb,amsthm,amscd packagesHigh Energy Physics - TheoryQuantum Algebratext