A Causal Algebra for Liouville Exponentials

TL;DR

This paper develops a causal algebra for Liouville exponentials on a cylinder, ensuring causality and local brackets, with a quantum realization that maintains these properties.

Contribution

It introduces a new causal Poisson bracket algebra for Liouville exponentials and provides a quantum realization that preserves causality and local structure.

Findings

Derived a causal Poisson bracket algebra for Liouville exponentials.

Established a quantum realization that maintains causality.

Ensured the algebra involves at least four space-time points.

Abstract

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of space-time points with a minimum of four. A quantum realisation of the algebra is obtained which preserves causality and the local form of non-equal time brackets.