Integrable quantum field theory with boundary

Subir Ghoshal

Patrick Dorey, Davide Fioravanti A, Chaiho P. Rim +1 more

Giuseppe Mussardo

Abstract Quantum field theory with boundaries is a very rich subject both from purely theoretical point of view or applicative aims. Chapter 21 presents the basis results relative to critical systems and massive integrable field theories. It covers stress-energy tensor in boundary conformal field theories and integrable deformations of these theories (including the single Virasoro algebra), reflection amplitudes, conformal boundary operators and states (including the Hilbert space and Ishibashi state), non-renormalizable states of the Hilbert space, operator product expansion involving a boundary operator, massive integrable boundary field theory, the massive boundary Ising model, boundary magnetic fields and correlation functions.

Marco Bellacosa

In this thesis we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theory with boundaries, with emphasis to sine-Gordon model with Dirichlet boundary conditions. Exact calculations of the dependence of the energy spectrum on the size and on boundary conditions are presented for vacuum and many excited states.

武夫 稲見, 隆 佐々木

André LeClair, Giuseppe Mussardo, Hubert Saleur +1 more

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.