Matrix elements of the operator Tbar{T} in integrable quantum field theory.pdf

a r X i v : h e p - t h / 0 4 0 7 1 4 2 v 2 2 6 J a n 2 0 0 5 SISSA 48/2004/FM Matrix elements of the operator T T? in integrable quantum field theory Gesualdo Delfino and Giuliano Niccoli International School for Advanced Studies (SISSA) via Beirut 2-4, 34014 Trieste, Italy INFN sezione di Trieste E-mail: delfino@sissa.it, niccoli@sissa.it Abstract Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T T? constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model. 1 Introduction It is commonly believed that the knowledge of the S-matrix implicitly amounts to the complete solution of a quantum field theory, in the sense that the off-shell physics (all operators and their correlation functions) can be reconstructed starting from the particle dynamics. The integrable theories in two dimensions are the only interacting quantum field theories which are exactly solved on shell, and then provide an unique framework for testing the status of this belief. The determination of the S-matrix in integrable theories follows from the combination of the general analyticity properties [1] with the elasticity and factorization of the scattering processes imposed by the existence of an infinite number of quantum integrals of motion [2]. Moving off-shell means evaluating the matrix elements (form factors) of the operators on the asymptotic particle states; if this is achieved the correlators can be expressed as spectral sums. The simpli- fications of the dynamics allow to prescribe the analytic properties of the form factors through a set of functional equations whose only input is the S-matrix [3, 4]. A sol