A classical vertex algebra constructed with the use of some logarithmic formal calculus

TL;DR

This paper introduces a new logarithmic formal calculus to construct a classical vertex algebra, providing a direct derivation of the Jacobi identity in a self-contained manner.

Contribution

It presents a novel logarithmic formal calculus approach to construct vertex algebras, simplifying the derivation of fundamental identities.

Findings

Successful construction of a classical vertex algebra using logarithmic calculus

Direct derivation of the Jacobi identity within the new framework

Self-contained method that enhances understanding of vertex algebra structures

Abstract

Using some new logarithmic formal calculus, we construct a well known vertex algebra, obtaining the Jacobi identity directly, in an essentially self-contained treatment.