Boundary Reflection Matrix in Perturbative Quantum Field Theory

TL;DR

This paper develops a method to compute the boundary reflection matrix in quantum field theory on a half line using perturbation theory, specifically for affine Toda models with Neumann boundary conditions.

Contribution

It introduces a perturbative approach to derive the boundary reflection matrix directly from two-point functions, addressing a specific factor ambiguity.

Findings

Successfully derived the boundary reflection matrix for affine Toda field theory

Identified a mysterious factor half in the boundary reflection matrix

Demonstrated the method's applicability to Neumann boundary conditions

Abstract

We study boundary reflection matrix for the quantum field theory defined on a half line using Feynman's perturbation theory. The boundary reflection matrix can be extracted directly from the two-point correlation function. This enables us to determine the boundary reflection matrix for affine Toda field theory with the Neumann boundary condition modulo `a mysterious factor half'.