Colour valued Scattering Matrices

We describe a general construction principle which allows to add colour values to a coupling constant dependent scattering matrix. As a concrete realization of this mechanism we provide a new type of S-matrix which generalizes the one of affine Toda field theory, being related to a pair of Lie algebras. A characteristic feature of this S-matrix is that in general it violates parity invariance. For particular choices of the two Lie algebras involved this scattering matrix coincides with the one related to the scaling models described by the minimal affine Toda S-matrices and for other choices with the one of the Homogeneous sine-Gordon models with vanishing resonance parameters. We carry out the thermodynamic Bethe ansatz and identify the corresponding ultraviolet effective central charges.Comment: 8 pages Latex, example, comment and reference adde

Braid Relations in Affine Toda Field Theory

We provide explicit realizations for the operators which when exchanged give rise to the scattering matrix. For affine Toda field theory we present two alternative constructions, one related to a free bosonic theory and the other formally to the quantum affine Heisenberg algebra of $U_q(\hat{Sl_2})$.Comment: 20 pages Late

PT-symmetric Deformations of the Korteweg-de Vries Equation

We propose a new family of complex PT-symmetric extensions of the Korteweg-de Vries equation. The deformed equations can be associated to a sequence of non-Hermitian Hamiltonians. The first charges related to the conservation of mass, momentum and energy are constructed. We investigate solitary wave solutions of the equation of motion for various boundary conditions.Comment: 11 pages, 3 figure

Couplings in Affine Toda Field Theories

We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra {\bf g}. All n-point couplings with $n \geq 4$ are completely determined in terms of the masses and the three-point couplings. A general fusing rule, formulated in the root space of the Lie algebra, is derived for all n-point couplings.Comment: 14 p., USP-IFQSC/TH/92-5

PT-symmetry and Integrability

We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to construct deformations of some integrable systems, the Calogero-Moser-Sutherland model and the Korteweg deVries equation. Some properties of these models are discussed.Comment: Proceeding of the Micro conference Analytic and algebraic methods II, Doppler Institute, Prague, April 200

Factorized Scattering in the Presence of Reflecting Boundaries

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.Comment: 18p., USP-IFQSC/TH/93-0

Boundary Bound States in Affine Toda Field Theory

We demonstrate that the generalization of the Coleman-Thun mechanism may be applied to the situation, when considering scattering processes in 1+1-dimensions in the presence of reflecting boundaries. For affine Toda field theories we find that the binding energies of the bound states are always half the sum over a set of masses having the same colour with respect to the bicolouration of the Dynkin diagram. For the case of $E_6$-affine Toda field theory we compute explicitly the spectrum of all higher boundary bound states. The complete set of states constitutes a closed bootstrap.Comment: 16 p., Late

Quantum, noncommutative and MOND corrections to the entropic law of gravitation

Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde’s entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a classical setting by seeking appropriate corrections in the entropy. We estimate the correction term by using concrete coherent states in the standard and generalized versions of Heisenberg’s uncertainty principle. Using Jackiw’s direct and analytic method, we compute the explicit wavefunctions for these states, producing minimal length as well as minimal products. Subsequently, we derive a further selection criterium restricting the free parameters in the model in providing a canonical formulation of the quantum corrected Newtonian law by setting up the Lagrangian and Hamiltonian for the system

The two dimensional harmonic oscillator on a noncommutative space with minimal uncertainties

The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken.Comment: 4 pages, contribution to proceedings of "Analytic and algebraic methods in physics X", Pragu