Boundary Exchange Algebras and Scattering on the Half Line

TL;DR

This paper explores the algebraic structures underlying quantum field scattering on a half-line with boundaries, introducing a new algebraic framework inspired by integrable models and boundary conditions.

Contribution

It introduces an associative algebra with exchange properties derived from scattering processes, and constructs Fock representations for boundary quantum field theories.

Findings

Established basic properties of the boundary exchange algebra.

Derived Fock representations associated with involutions.

Applied algebraic framework to construct quantum fields and analyze scattering.

Abstract

Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting boundary conditions on the half line. The basic properties of this algebra are established and the Fock representations associated with certain involutions are derived. We apply these results for the construction of quantum fields and for the study of scattering on the half line.