International Journal of Modern Physics A

We discuss the algebraic structure of the spin chains related to high energy scattering in QCD. We study the sl(2) Yangian symmetry and possible generalizations to nonzero spin and anisotropy parameter.

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear Abelian gauge theory in two dimensions. The soluble models in this method are extended to a wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture, so this analysis might shed some light on the analysis of gravitational theory and nonpolynomial field theories.

We investigate the natural occurrence of exponentially small couplings in effective field theories deduced from higher-dimensional models. As a concrete example we calculate the coupling between twisted fields of the Z₃ Abelian orbifold compactification of the heterotic string. These are described by an effective field theory coupling the ten-dimensional massless gauge bosons to the four-dimensional twisted fields. The propagation of massive winding modes between the fixed points of the orbifold induces exponentially small couplings between the massless twisted fields. The resulting small couplings have an exponential dependence on the mass of the intermediate states and the distance between the fixed points.

The system of N scalar particles with Grassman-valued color changes plus the color SU(3) Yang–Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the Wigner-covariant rest frame instant form of dynamics (covariant Coulomb gauge) is given. From the reduced Hamilton equations we extract the second order equations of motion for both the reduced transverse color field and the particles. Then we study this relativistic scalar quark model, deduced from the classical QCD Lagrangian and with the color field present, in the N=2 (meson) case. A special form of the requirement of having only color singlets, suited for a field-independent quark model, produces a "pseudoclassical asymptotic freedom" and a regularization of the quark self-energy.

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.

Nonleptonic decays of B mesons into two mesons or meson resonances are studied on the basis of two versions of simple pole dominance models involving scalar, vector, pseudoscalar and axial vector poles. The results are compared with those obtained from the usual factorization model and are used to obtain information on strong coupling constants between the B meson and one light or one charmed meson, respectively. These coupling constants are compared to results from various QCD sum rule calculations.