Boundary conditions changing operators in non conformal theories

TL;DR

This paper develops an axiomatic framework to analyze boundary condition changing operators in non-conformal, integrable quantum field theories with mass scales, providing explicit scalar product calculations for the Ising and sinh-Gordon models.

Contribution

It introduces a novel axiomatic approach to scalar products between states with different boundary conditions in non-conformal integrable models, with explicit computations for specific models.

Findings

Explicit scalar products for Ising and sinh-Gordon models.

New exact results for transition probabilities in dissipative quantum mechanics.

Framework applicable to inhomogeneous boundary conditions and quantum impurity problems.

Abstract

Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More precisely, we propose an axiomatic approach to determine the general scalar products ${}_b<\theta_1, ... ,\theta_m||\theta'_1, ... ,\theta'_{n}>_a$ between asymptotic states in the Hilbert spaces with $a$ and $b$ boundary conditions respectively, and compute these scalar products explicitely in the case of the Ising and sinh-Gordon models with a mass and a boundary interaction. These quantities can be used to study statistical systems with inhomogeneous boundary conditions, and, more interestingly maybe, dynamical problems in quantum impurity problems. As an example, we obtain a series of new exact results for the transition probability in the double well problem of dissipative quantum mechanics.