On axioms for a vertex algebra and the locality of quantum fields

TL;DR

This paper investigates the fundamental axioms of vertex algebras and proves key identities related to the locality of quantum fields, providing new insights and characterizations in the theory of vertex algebras.

Contribution

It offers a direct proof of Li's theorem on local systems of vertex operators and discusses various characterizations of vertex algebras.

Findings

Proof of the Cauchy-Jacobi (Borcherds) identity for mutually local fields

A direct proof of Li's theorem on local vertex operator systems

Multiple characterizations of vertex algebras

Abstract

The 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.