Boundary conditions changing operators in non conformal theories

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 ${}_b<θ_1, ... ,θ_m||θ'_1, ... ,θ'_{n}>_a$ 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.