Thermodynamic Bethe Ansatz for Excited States

Abstract

In these lectures I am going to discuss Integrable Quantum Field Theories in two dimensions. Integrable QFT possess infinite series of commuting local Integrals of Motion (IM). Relatively simple but very important Integrable QFT are Conformal Field Theories (CFT). More general non-conformal Integrable QFT are obtained by perturbing CFT with suitably chosen relevant operators [1]. These Integrable Perturbed CFT (PCFT) are typically massive QFT and their exact on-shell solutions can be given in terms of Factorizable S-matrices [1,2]. The off-shell information although encoded in the S-matrix is much more difficult to extract. Very interesting off-shell characteristic of QFT is its finite-size energy spectrum, e.g. the spectrum of its Hamiltonian in the situation when the spatial coordinate is compactified on a circle of circumference R. Important progress towards calculating this spectrum has been made lately with the help of Thermodynamic Bethe Ansatz (TBA) technique [3]. This approach allows one to obtain the ground-state energy E ₀(R) of the finite-size system provided the on-shell solution is known, the problem being reduced to solving non-linear integral equations (TBA equations).