Quantum field theories in finite volume: Excited state energies Original Research Article

We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with the spatial coordinate compactified on a circle of circumference R. The IQFT “commuting transfer matrices” introduced earlier [Commun. Math. Phys. 177 (1996) 381] for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator Φ1,3. We study the models in which the fusion relations for these “transfer matrices” truncate and provide closed integral equations which generalize the equations of the thermodynamic Bethe ansatz to excited states. The explicit calculations are done for the first excited state in the “scaling Lee-Yang model”.