Geometric Interpretations of Quandle Homology

Geometric representations of cycles in quandle homology theory are given in terms of colored knot diagrams. Abstract knot diagrams are generalized to diagrams with exceptional points which, when colored, correspond to degenerate cycles. Bounding chains are realized, and used to obtain equivalence moves for homologous cycles. The methods are applied to prove that boundary homomorphisms in a homology exact sequence vanish.Comment: 27 Figures 35 page

Relativistic effects in neutron-deuteron elastic scattering

We solved the three-nucleon Faddeev equation including relativistic features such as relativistic kinematics, boost effects and Wigner spin rotations. As dynamical input a relativistic nucleon-nucleon interaction exactly on-shell equivalent to the AV18 potential has been used. The effects of Wigner rotations for elastic scattering observables were found to be small. The boost effects are significant at higher energies.They diminish the transition matrix elements at higher energies and lead in spite of the increased relativistic phase-space factor as compared to the nonrelativistic one to rather small effects in the cross section, which are mostly restricted to the backward angles.Comment: 27 pages, 5 Postscript figure

Partial Wave Decomposition for Meson Exchange Currents in Few-Nucleon Systems

We develop an approach for calculating matrix elements of meson exchange currents between 3N basis states in (jJ)-coupling and a 3N bound state. The contribution generated by $\pi$- and $\rho$-exchange are included in the consideration. The matrix elements are expressed in terms of multiple integrals in the momentum space. We apply a technique of the partial wave decompositions and carry out some angular integrations in closed form. Different representations appropriate for numerical calculations are derived for the matrix elements of interest. The momentum dependences of the matrix elements are studied and benchmark results are presented. The approach developed is of interest for the investigations of deuteron- proton radiative capture and ^3He photo- and electrodisintegration when the interaction in the initial or final nuclear states is taken into account by solving the Faddeev equations.Comment: 32pages (14 figures