We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of "maximal analyticity" and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the "off-shell" Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the Sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.

Using Watson's and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field φ(x) and the stress-energy tensor T µν (x) of Sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of T µν (x) to the sum rule of the c-theorem.

It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a non-observable operator as it ceases to be quasi-Hermitian when the metric becomes time-dependent.

Deformations of the canonical commutation relations lead to non-Hermitian momentum and position operators and therefore almost inevitably to non-Hermitian Hamiltonians. We demonstrate that such type of deformed quantum mechanical systems may be treated in a similar framework as quasi/pseudo and/or PT -symmetric systems, which have recently attracted much attention. For a newly proposed deformation of exponential type we compute the minimal uncertainty and minimal length, which are essential in almost all approaches to quantum gravity.

We apply the thermodynamic Bethe Ansatz to investigate the high energy behaviour of a class of scattering matrices which have recently been proposed to describe the Homogeneous sine-Gordon models related to simply laced Lie algebras. A characteristic feature is that some elements of the suggested Smatrices are not parity invariant and contain resonance shifts which allow for the formation of unstable bound states. From the Lagrangian point of view these models may be viewed as integrable perturbations of WZNW-coset models and in our analysis we recover indeed in the deep ultraviolet regime the effective central charge related to these cosets, supporting therefore the S-matrix proposal. For the SU (3) k -model we present a detailed numerical analysis of the scaling function which exhibits the well known staircase pattern for theories involving resonance parameters, indicating the energy scales of stable and unstable particles. We demonstrate that, as a consequence of the interplay between the mass scale and the resonance parameter, the ultraviolet limit of the HSG-model may be viewed alternatively as a massless ultraviolet-infrared-flow between different conformal cosets. For k = 2 we recover as a subsystem the flow between the tricritical Ising and the Ising model.

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the W-matrix, which encodes the reflection of a particle off a wall.This set of equations is sufficient to derive explicit formulas for W , which we illustrate in the case of some particular affine Toda field theories.

Contribution from H. F. Jones I'll be more enthusiastic about encouraging thinking outside the box when there's evidence of any thinking going on inside it.

We investigate a quantum mechanical system on a noncommutative space for which the structure constant is explicitly time-dependent. Any autonomous Hamiltonian on such a space acquires a time-dependent form in terms of the conventional canonical variables. We employ the Lewis-Riesenfeld method of invariants to construct explicit analytical solutions for the corresponding time-dependent Schrödinger equation.The eigenfunctions are expressed in terms of the solutions of variants of the nonlinear Ermakov-Pinney equation and discussed in detail for various types of background fields. We utilize the solutions to verify a generalized version of Heisenberg's uncertainty relations for which the lower bound becomes a time-dependent function of the background fields. We study the variance for various states including standard Glauber coherent states with their squeezed versions and Gaussian Klauder coherent states resembling a quasi-classical behaviour. No type of coherent states appears to be optimal in general with regard to achieving minimal uncertainties, as this feature turns out to be background field dependent.