Abstract:
The non-perturbative mapping between different Quantum Field Theories and other features of two-dimensional massive integrable models are discussed by using the Form Factor approach. The computation of ultraviolet data associated to the massive regime is illustrated by taking as an example the scattering theory of the Ising Model with boundary.

Abstract:
In this talk I discuss the form factor approach used to compute correlation functions of integrable models in two dimensions. The Sinh-Gordon model is our basic example. Using Watson's and the recursive equations satisfied by matrix elements of local operators, I present the computation of the form factors of the elementary field $\phi(x)$ and the stress-energy tensor $T_{\mu\nu}(x)$ of the theory.

Abstract:
A simple criterion is derived in order that a number sequence ${\cal S}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is explicitly computed in a semi-classical approximation. The existence of such a potential implies that the primality testing can in principle be resolved by the sole use of physical laws.

Abstract:
The lowest representatives of the Form Factors relative to the trace operators of N=1 Super Sinh-Gordon Model are exactly calculated. The novelty of their determination consists in solving a coupled set of unitarity and crossing equations. Analytic continuations of the Form Factors as functions of the coupling constant allows the study of interesting models in a uniform way, among these the latest model of the Roaming Series and the minimal supersymmetric models as investigated by Schoutens. A fermionic version of the $c$-theorem is also proved and the corresponding sum-rule derived.

Abstract:
We discuss the determination of the lowest Form Factors relative to the trace operators of N=1 Super Sinh-Gordon Model. Analytic continuations of these Form Factors as functions of the coupling constant allows us to study a series of models in a uniform way, among these the latest model of the Roaming Series and a class of minimal supersymmetric models.

Abstract:
We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies $\alpha$ and $\beta$. Looking at the theory as a perturbed Sine-Gordon model, we use Form Factor Perturbation Theory to analyse the evolution of the spectrum of particle excitations. We show how, within this formalism, the non-locality of the perturbation with respect to the solitons is responsible for their confinement in the perturbed theory. The effects of the frequency ratio $\alpha/\beta$ being a rational or irrational number and the occurrence of massless flows from the gaussian to the Ising fixed point are also discussed. A generalisation of the Ashkin-Teller model and the massive Schwinger model are presented as examples of application of the formalism.

Abstract:
The two-point correlation function of the stress-energy tensor for the $\Phi_{1,3}$ massive deformation of the non-unitary model ${\cal M}_{3,5}$ is computed. We compare the ultraviolet CFT perturbative expansion of this correlation function with its spectral representation given by a summation over matrix elements of the intermediate asymptotic massive particles. The fast rate of convergence of both approaches provides an explicit example of an accurate interpolation between the infrared and ultraviolet behaviours of a Quantum Field Theory.

Abstract:
We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of disorder operators in a free theory of complex bosonic and fermionic field, correlators ruled by a Painleve differential equation.

Abstract:
The form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function $<\sigma(x) \sigma(0)>$ of the two-dimensional Ising model in a magnetic field at $T=T_c$. The matrix elements of the magnetization operator $\sigma(x)$ present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function.