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We investigate the chiral properties of near-zero modes for thick classical center vortices in $SU(2)$ lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.

We find, in close analogy to Abelian dominance in the maximal Abelian gauge, the phenomenon of center dominance in the maximal center gauge for SU(2) lattice gauge theory. The maximal center gauge is a gauge-fixing condition that preserves a residual ${Z}_{2}$ gauge symmetry; ``center projection'' is the projection of SU(2) link variables onto ${Z}_{2}$ center elements, and ``center dominance'' is the fact that the center-projected link elements carry most of the information about the string tension of the full theory. We present numerical evidence that the thin ${Z}_{2}$ vortices of the projected configurations are associated with ``thick'' ${Z}_{2}$ vortices in the unprojected configurations. The evidence also suggests that the thick ${Z}_{2}$ vortices may play a significant role in the confinement process.

We analyze topological charge contributions from classical $SU(2)$ center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of $F\stackrel{\texttildelow{}}{F}$ in the plaquette or hypercube definitions and the lattice index theorem. For the latter the zero modes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations are investigated. We find several problems for the individual definitions and discuss the discrepancies between the different topological charge definitions. Our results show that the interpretation of topological charge in the background of center vortices is rather subtle.

We investigate the free energy distribution across the interface of coexisting quark and hadron matter in the framework of lattice QCD. We calculate the interface tension [alpha] with the differential method'' for pure SU(3) gauge theory and in the presence of dynamical quarks with four flavors. Using lattices with a spatial volume 8[sup 2][times]16 we discuss the agreement between the differential and integral method in the pure gluonic case. With dynamical fermions it turns out that the interface tension is very small and we estimate an upper bound of [alpha]/[ital T][sub [ital c]][sup 3][lt]0.1. The chiral condensate indicates the same width of the domain wall as the Polyakov loop distribution and the other thermodynamical observables under consideration.

For the {beta}{sup -}-decay of the neutron we analyze the continuum-state and bound-state decay modes. We calculate the decay rates, the electron energy spectrum for the continuum-state decay mode, and angular distributions of the decay probabilities for the continuum-state and bound-state decay modes. The theoretical results are obtained for the new value for the axial coupling constant g{sub A}=1.2750(9), obtained recently by H. Abele [Prog. Part. Nucl. Phys. 60, 1 (2008)] from the fit of the experimental data on the coefficient of the correlation of the neutron spin and the electron momentum of the electron energy spectrum of the continuum-state decay mode. We take into account the contribution of radiative corrections and the scalar and tensor weak couplings. The calculated angular distributions of the probabilities of the bound-state decay modes of the polarized neutron can be used for the experimental measurements of the bound-state {beta}{sup -}-decays into the hyperfine states with total angular momentum F=1 and scalar and tensor weak coupling constants.

We calculate the decay rates lambda_(beta^-_c) and lambda_(beta^-_b) of the continuum- and bound-state beta^- decays for bare 205Hg80+ and 207Tl81+ ions. For the ratio of the decay rates R_(b/c) = lambda_(beta^-_b)/lambda_(beta^-_c) we obtain the values R_(b/c) = 0.161 and R_(b/c) = 0.190 for bare 205Hg80+ and 207Tl81+ ions, respectively. The theoretical value of the ratio R_(b/c) = 0.190 for the decays of 207Tl81+ agrees within 1% of accuracy with the experimental data R^exp_(b/c) = 0.188(18), obtained at GSI. The theoretical ratio R_(b/c) = 0.161 for 205Hg80+ is about 20% smaller than the experimental value R^exp_(b/c) = 0.20(2), measured recently at GSI.

The nuclear K-shell electron-capture (EC) and positron ({beta}{sup +}) decay constants, {lambda}{sub EC} and {lambda}{sub {beta}{sup +}} of H-like {sup 140}Pr{sup 58+} and He-like {sup 140}Pr{sup 57+} ions, measured recently in the experimental storage ring (ESR) at GSI, were calculated using standard weak interaction theory. The calculated ratios R={lambda}{sub EC}/{lambda}{sub {beta}{sup +}} of the decay constants agree with the experimental values within an accuracy better than 3%.

Using the experimental data on the energy-level shift of kaonic hydrogen in the ground state [Beer et al., Phys. Rev. Lett. 94, 212302 (2005)] and the theoretical value of the energy-level shift, calculated within the phenomenological quantum field theoretic approach to the description of strong low-energy $\overline{K}N$ and $\overline{K}NN$, interactions, we estimate the value of the ${\ensuremath{\sigma}}_{KN}^{(I=1)}(0)$ term of low-energy $\overline{K}N$ scattering. We get ${\ensuremath{\sigma}}_{KN}^{(I=1)}(0)=433\ifmmode\pm\else\textpm\fi{}132\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. This shows the absence of strange quarks in the proton structure.

We calculate the radiative transition rates np{yields}1s+{gamma} in kaonic hydrogen and kaonic deuterium, induced by strong low-energy interactions and enhanced by Coulomb interactions. The obtained results should be taken into account for the theoretical analysis of the experimental data on the x-ray spectra and yields in kaonic atoms.

We consider a model of topological solitons where charged particles have finite mass and the electric charge is quantised already at the classical level. In the electrodynamic limit, which physically corresponds to electrodynamics of solitons of zero size, the Lagrangian of this model has two degrees of freedom only and reduces to the Lagrangian of the Maxwell field in dual representation. We derive the equations of motion and discuss their relations with Maxwell's equations. It is shown that Coulomb and Lorentz forces are a consequence of topology. Further, we relate the U(1) gauge invariance of electrodynamics to the geometry of the soliton field, give a general relation for the derivation of the soliton field from the field strength tensor in electrodynamics and use this relation to express homogeneous electric fields in terms of the soliton field., Comment: 13 pages, 4 figures, Introduction and Section II (Model Lagrangian) rewritten, new chapters concerning electrodynamic limit and discussion of causality inserted

We discuss the derivation of the path integral representation over gauge degrees of freedom for Wilson loops in $\mathrm{SU}(N)$ gauge theory and 4-dimensional Euclidean space-time by using well-known properties of group characters. A discretized form of the path integral is naturally provided by the properties of group characters and does not need any artificial regularization. We show that the path integral over gauge degrees of freedom for Wilson loops derived by Diakonov and Petrov [Phys. Lett. B 224 131 (1989)] by using a special regularization is erroneous and predicts zero for the Wilson loop. This property is obtained by direct evaluation of path integrals for Wilson loops defined for pure $\mathrm{SU}(2)$ gauge fields and $Z(2)$ center vortices with spatial azimuthal symmetry. Further we show that both derivations given by Diakonov and Petrov for their regularized path integral, if done correctly, predict also zero for Wilson loops. Therefore, the application of their path integral representation of Wilson loops cannot give a new way to check confinement in lattice as has been declared by Diakonov and Petrov [Phys. Lett. B 242 425 (1990)]. From the path integral representation which we consider we conclude that no new non-Abelian Stokes theorem can exist for Wilson loops except the old-fashioned one derived by means of the path-ordering procedure.

This paper reports studies of the dependence of the ..cap alpha..-emission probability for transitional, rare-earth, and actinide nuclei on changes of deformation at very high angular momenta. It has been found that often nuclei are trapped into configurations with anomalously large stability against ..cap alpha.. emission at spins below the fission instability. The effect, if observed in experiment, could yield a direct test of the theoretically predicted large shape changes in the rotating nucleus.

Multiquark systems up to six static charges are studied within the framework of SU(3) gauge theory on a lattice with dimension 16 x 16 x 16 x 6 and hot boundary conditions. Correlations between the quarks of a hadron are computed as well as hadron-hadron correlations. We find a confining potential acting between color-nonsinglet--color-nonsinglet systems, whereas the gluon exchange can mediate no force if one of the interacting clusters is a color singlet and pointlike.