Boundary energy and boundary states in integrable quantum field theories

TL;DR

This paper investigates the ground state energy of integrable 1+1 dimensional quantum field theories with boundaries, introducing new methods and deriving exact results for various models including sine-Gordon and Ising.

Contribution

It develops a novel R-channel TBA approach for scalar theories and generalizes existing methods to non-scalar models, providing exact formulas and boundary state analyses.

Findings

Derived formulas for boundary state scalar products and normalization.

Obtained exact partition functions for the critical Ising model with boundary magnetic field.

Analyzed energy spectra, excited states, and boundary S-matrices for various models.

Abstract

We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S-matrix of $O(n)$ and minimal models.