A representation of the exchange relation for affine Toda field theory

TL;DR

This paper constructs vertex operator representations for affine Toda field theory exchange relations, linking S-matrix bootstrap relations to conserved quantities through an algebraic framework.

Contribution

It introduces a novel algebraic construction of vertex operators that encode the exchange relations and automatically derive bootstrap relations from conserved quantities.

Findings

Vertex operators represent exchange relations involving affine Toda S-matrices.

Bootstrap relations follow automatically from conserved quantities.

The approach provides an algebraic interpretation of particle fusion processes.

Abstract

Vertex operators are constructed providing representations of the exchange relations containing either the S-matrix of a real coupling (simply-laced) affine Toda field theory, or its minimal counterpart. One feature of the construction is that the bootstrap relations for the S-matrices follow automatically from those for the conserved quantities, via an algebraic interpretation of the fusing of two particles to form a single bound state.