Integrable Quantum Field Theories in Finite Volume: Excited State Energies

Abstract

We develop a method of computing the excited state energies in Integrable Quantum Field Theories (IQFT) in finite geometry, with spatial coordinate compactified on a circle of circumference R. The IQFT ``commuting transfer-matrices'' introduced by us (BLZ) for Conformal Field Theories (CFT) are generalized to non-conformal IQFT obtained by perturbing CFT with the operator ${\Phi }_{1,3}$. We study the models in which the fusion relations for these ``transfer-matrices'' truncate and provide closed integral equations which generalize the equations of Thermodynamic Bethe Ansatz to excited states. The explicit calculations are done for the first excited state in the ``Scaling Lee-Yang Model''.

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References in corpus (6)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Dilogarithm identities
• Exact perturbative solution of the Kondo problem
• Generalized KdV and Quantum Inverse Scattering Description of Conformal Minimal Models

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