A bstract Quantum sinh-Gordon model in 1 + 1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as a pile of planes connected to each other along cut lines. The cut lines end at branch points, which are represented by a twist operator
Tn T n . Operators of such kind are interesting in the framework of the problem of computing von Neumann and Renyi entanglement entropies in the original model on the plane. The composite branch-point twist operators (CTO) are a natural generalization of the twist operators, obtained by placing a local operator to a branch point by means of a certain limiting procedure. Correlation function in quantum field theory can be, in principle, found by means of the spectral decomposition. It allows one to express them in terms of form factors of local operators, i.e. their matrix elements in the basis of stationary states. In integrable models complete sets of exact form factors of all operators can be found exactly as solutions of a system of bootstrap equations. Nevertheless, identification of these solution to the operators in terms of the basic fields remains problematic. In this work, we develop a technique of computing form factors of a class of CTO determined in terms of the basic field in the semiclassical approximation.
The scaling limit of the two-dimensional Ising model above the critical temperature is considered as an example for relativistic quantum theories on two-dimensional Minkowski space exhibiting a factorizing S -matrix. In this model, a recently proposed criterion for the existence of local quantum field theories with a prescribed factorizing scattering matrix is verified, thereby establishing a new constructive approach to two-dimensional quantum field theory in a particular example. The existence proof is accomplished by analysing the nuclearity properties of certain specific subsets of fermionic Fock spaces, and yields as a byproduct also a verification of the energy nuclearity condition of Buchholz and Wichmann in models of free fermions in four spacetime dimensions.
We solve the SU(N)-invariant Yang-Baxter equations imposing only the unitarity condition. The usual S matrices should satisfy the crossing symmetry which originates from the CPT invariance of relativistic quantum-field theory. In this paper, we consider nonrelativistic SU(N)-invariant factorizable S matrices by relaxing the crossing symmetry and making the amplitudes for creating and annihilating new particles vanish and find that these S matrices are exactly the same as those of the multicomponent Calogero-Sutherland model, the quantum-mechanical model with the hyperbolic potential between particles and antiparticles. This particular solution is of interest since it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations. \textcopyright{} 1996 The American Physical Society.