Chiral Charged Fermions, One Dimensional Quantum Field Theory and Vertex Algebra

TL;DR

This paper provides an explicit $L^2$-representation of chiral charged fermions, connecting them to vertex algebras and one-dimensional quantum field theory, with rigorous definitions in the compact case.

Contribution

It introduces a new explicit $L^2$-representation of chiral charged fermions and explores their role in the functional analytic framework of vertex algebras.

Findings

Explicit $L^2$-representation of chiral charged fermions.

Rigorous definition of unsmeared fermion operators inside the unit circle.

Connection between chiral fermions and vertex algebra structures.

Abstract

We give an explicit $L^2$-representation of chiral charged fermions using the Hardy-Lebesgue octant decomposition. In the " pure" case such a representation was already used by M. Sato in holonomic field theory. We study both "pure" and " mixed" cases. In the compact case we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions we orient our findings towards a functional analytic study of vertex algebras as one dimensional quantum field theory.