Smeared and unsmeared chiral vertex operators

TL;DR

This paper investigates the mathematical properties of chiral vertex operators, establishing their boundedness or unboundedness using elementary bosonic Fock space methods, with implications for quantum field theory and vertex operator algebras.

Contribution

It provides the first rigorous analysis of smeared and unsmeared chiral vertex operators' boundedness properties using elementary techniques.

Findings

Unboundedness of unsmeared chiral vertex operators.

Boundedness of smeared chiral vertex operators.

Potential applications to conformal quantum field theory and vertex operator algebra interpretation.

Abstract

We prove unboundedness and boundedness of the unsmeared and smeared chiral vertex operators, respectively. We use elementary methods in bosonic Fock space, only. Possible applications to conformal two - dimensional quantum field theory, perturbation thereof, and to the perturbative construction of the sine-Gordon model by the Epstein-Glaser method are discussed. From another point of view the results of this paper can be looked at as a first step towards a Hilbert space interpretation of vertex operator algebras.