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The relation between center vortices and fractional topological charge has been studied in this work. Specifically, we investigate a vortex configuration with fractional topological charge analyzing the lowest modes of the adjoint Dirac operator in both overlap and staggered formulations. We discuss the effects leading to chiral symmetry breaking.

The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the "preparation region", into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schr\"odinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The eventual influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions., Comment: 24 pages, 43 figures

Gauge fields control the dynamics of fermions, also a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also with the presence of fermionic fields., New data and new evaluations with different coaouthors. This version is submitted to MDPI / Universe

New analysis regarding the structure of center vortices and their color structure is presented: Using data from gluonic SU(2) lattice simulation with Wilson action a correlation of fluctuations in color space to curvature of vortex fluxes was found. Finite size effects of the S2-homogeneity hint at color homogeneous regions on the vortex surface.

The center vortex model of the QCD vacuum is very successful in explaining the non-perturbative properties of QCD, especially confinement, chiral symmetry breaking and the topological charge of vacuum configurations. On the other hand, the center vortex model still suffers from a Gribov problem: Direct maximal center gauge and center projection can lead to an underestimation of the string tension in smooth configurations or after persistent simulated annealing. We discuss methods to identify center regions, whose boundaries evaluate to center elements, and want to improve the vortex detection: these regions might help to recognize vortices in configurations where maximal center gauge lost the vortex finding property.

The computations of solutions of the field equations in the Model of Topological Particles, formulated with a scalar SU(2)-field, have shown instabilities leading to discrepancies between the numerical and analytical solutions. We identify the origin of these deviations in misalignments of the rotational axes corresponding to the SU(2) elements. The system of a single soliton we use as an example to show that a constraint suppressing the wave-like disturbances is able to lead to excellent agreement between the result of the numerical minimisation procedure and the analytical solution.

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions&mdash, that is, regions whose boundary evaluates to a nontrivial center element&mdash, a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

We review important aspects of QCD in the continuum and on the lattice and take a look at the fate of its symmetries with an emphasis on chiral symmetry breaking on the lattice., Comment: 5 figures added

The center vortex model, capable of explaining confinement and chiral symmetry breaking, has been plagued by the lattice equivalent of Gribov copies: different maxima of the gauge functional lead to different predictions of the string tension. It is possible to resolve this problem using center regions, loops evaluating to center elements, as guide for the gauge fixing procedure. The success of this approach was already shown, but the algorithms came with an arbitrary free parameter. In recent development this parameter has been fixed, even improving the results.

We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. We find some evidence for fractional topological charge during cooling the spherical center vortex on a [Formula: see text] lattice. We identify the object with topological charge [Formula: see text] as a Dirac monopole with a gauge field fading away at large distances. Therefore, even for periodic boundary conditions, it does not need an anti-monopole.

We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the incidence direction. As a main result of our calculation we obtain in addition to the well-known alteration of the radial distance a time dependent correction term for the phase modifying the circular motion of the particle. A background of gravitational waves creates some kind of uncertainty., Comment: Figures adjusted to correction term for the angular velocity, and references added

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 vorex 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 colorful spherical vortex and instanton ensembles have very similar Dirac eigenmodes and 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 influence of the magnetic vortex fluxes on quarks and how center vortices may break chiral symmetry.

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 analyse the hypothesis that the “GSI oscillations” of the K-shell electron capture decay (EC) rates of the H-like heavy ions are caused by quantum beats from a coherent state of two closely spaced ground mass-eigenstates and of decaying H-like heavy ions. We apply this mechanism to the calculation of the -decay rates of the H-like heavy ions and discuss the dynamics of the production of the H-like heavy ions with two closely spaced ground mass-eigenstates at GSI experiments. We show that such a mechanism cannot describe simultaneously the experimental data on both the EC-decay and -decay rates of the H-like heavy ions, measured at GSI.

We develop an analytical approach for studying lattice gauge theories within the plaquette representation where the plaquette matrices play the role of the fundamental degrees of freedom. We start from the original Batrouni formulation and show how it can be modified in such a way that each non-Abelian Bianchi identity contains only two connectors instead of four. In addition, we include dynamical fermions in the plaquette formulation. Using this representation we construct the low-temperature perturbative expansion for U ( 1 ) and SU ( N ) models and discuss its uniformity in the volume. The final aim of this study is to give a mathematical background for working with non-Abelian models in the plaquette formulation.

Within the effective quark model with chiral U (3) × U (3) symmetry we calculate the S-wave and P-wave amplitudes of the nonleptonic decay Σ+ → pπ0, the partial width and the dynamical polarization of the proton in the dependence on the polarization of the Σ+-hyperon. The theoretical results agree well with the experimental data.

We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the winding number between the two vacua, leading to a topological charge $Q=-1$ in the continuum. After growing temporal extent of these vortices, the lattice topological charge approaches $-1$ and the index theorem is fulfilled. We analyze the low lying modes of the overlap Dirac operator in the background of these colorful plane vortices and compare them with those of spherical vortices. They show characteristic properties for spontaneous chiral symmetry breaking., 15 pages, 14 figures

We analyse the renormalizability of the sine-Gordon model using the two-point causal Green function. We show that all divergences can be removed by the renormalization of the dimensional coupling constant using the renormalization constant Z1, calculated in Faber and Ivanov (2003 J. Phys. A: Math. Gen. 36 7839) within the path-integral approach. We calculate the Gell-Mann–Low function and solve the Callan–Symanzik equation for the two-point Green function. We analyse the renormalizability of Gaussian fluctuations around a soliton. We show that Gaussian fluctuations around a soliton solution are renormalized like quantum fluctuations around the trivial vacuum and do not introduce any singularity to the sine-Gordon model at β2 = 8π. We calculate the correction to the soliton mass, caused by Gaussian fluctuations around a soliton, within the discretization procedure for various boundary conditions and find complete agreement with our result, obtained in continuous space–time.

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a^0_0 and a^1_0 of bar-KN scattering with isospin I=0 and I = 1 satisfy the low-energy theorem a^0_0 + 3 a^1_0 = 0 valid to leading order in chiral expansion. In the model of strong low-energy bar-KN interactions at threshold (EPJA 21,11 (2004)) we revisit the contribution of the Sigma(1750) resonance, which does not saturate the low-energy theorem a^0_0 + 3 a^1_0 = 0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S-wave scattering amplitudes of K^-N and K^-d scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and kaonic deuterium. The result obtained for kaonic hydrogen agrees well with recent experimental data by the DEAR Collaboration. We analyse the cross sections for elastic and inelastic K^-p scattering for laboratory momenta of the incident K^- meson from the domain 70 MeV/c < p_K < 150 MeV/c. The theoretical results agree with the available experimental data within two standard deviations., 20 pages, Latex, We have slightly corrected the contribution of the double scattering. This changes the S-wave scattering length of K^-d scattering by 17%, which is commensurable with the theoretical uncertainty

We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole positions. We find periodic deviations from the $1/r$-behavior of the monopole-antimonopole potential leading to local extrema. We suppose that these meta-stabilities may influence the order of the phase transition in compact QED., Comment: 11 pages, 5 figures

The energy level displacements of the excited nl states of pionic hydrogen and the contribution of the ns -> 1s transitions and the (pi^-p)_Coul -> 1s transitions of the pi^-p pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach developed in nucl-th/0306047., 18 pages, no figures, latex, text is revised, references are added

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model., Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics A

A BCS-type wave function describes the ground state of the massless Thirring model in the chirally broken phase. The massless Thirring model with fermion fields quantized in the chirally broken phase bosonizes to the quantum field theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723 (2001)). The wave functions of the ground state of the free massless (pseudo)scalar field are obtained from the BCS-type wave function by averaging over quantum fluctuations of the Thirring fermion fields. We show that these wave functions are orthogonal, normalized and non-invariant under shifts of the massless (pseudo)scalar field. This testifies the spontaneous breaking of the field-shift symmetry in the quantum field theory of a free massless (pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude calculated for the bosonized BCS-type wave functions coincides with the generating functional of Green functions defined only by the contribution of vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the assumption that the bosonized BCS-type wave function is defined by the collective zero-mode (hep-th/0212226). We argue that the obtained result is not a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems., 9 pages, Latex, no figures, Revised according to the version accepted for publication in Physics Letters B

We analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from classical center vortices in SU(2) lattice gauge theory. We show that colorful spherical vortex and instanton configurations have very similar Dirac eigenmodes and 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 influence of the magnetic vortex fluxes on quarks and how center vortices may break chiral symmetry., Comment: Prepared for the 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3 in Mainz, Germany

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin-Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows to identify the topological charge in the sine-Gordon model with the fermion number., Comment: 62 pages, 3 figures,misprints are corrected, the chiral Jacobian is recalculated and a few references are added

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.

The Nambu–Jona–Lasinio model of the deuteron suggested by Nambu and Jona–Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron–proton collective excitation, i.e. a Cooper np–pair, induced by a phenomenological local four–nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one–nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon–loop anomalies which are completely determined by one–nucleon loop diagrams. The dominance of contributions of nucleon–loop anomalies to effective Lagrangians of low–energy nuclear interactions is justified in the large NC expansion, where NC is the number of quark colours.

Interquark confinement potential is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings as a functional of a dual Dirac string length. The calculation is carried out by the explicit integration over quantum fluctuations of a dual-vector field (monopole-antimonopole collective excitation) around the Abrikosov flux line and string shape fluctuations. The contribution of the scalar field (monopole-antimonopole collective excitation) exchange is taken into account in the tree approximation due to the London limit regime., 10 pages, Latex, no figures

The magnetic monopole condensate is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings suggested in Refs.[1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole-antimonopole collective excitation field. The integration over quantum fluctuations of the dual-vector monopole-antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate., Comment: 19 pages, Latex, 2 figures

We investigate singly and doubly charged flux tubes in U(1) lattice gauge theory. By simulating the dually transformed path integral we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without loss of numerical precision. We simulate flux tubes between static sources as well as periodically closed flux tubes, calculating flux tube profiles, the total field energy and the free energy. Our main results are that the string tension in both three and four dimensions scales proportionally to the charge -- which is in contrast to previous lattice results -- and that in four-dimensional U(1) there is an attractive interaction between flux tubes for beta approaching the phase transition., Comment: 19 pages, latex2e with tex- and eps-figures; complete postscript file also available at ftp://is1.kph.tuwien.ac.at/pub/zach/np97.ps.gz

The string shape fluctuations are integrated out in a dual Higgs model with dual Dirac strings. The effective string energy is calculated. By applying the ζ-function regularization it is shown that a Coulomb-like contribution has a standard form −α string L , where L is a length of a string and α string = π 12 for opened strings. For closed strings one gets α string = π 3 .

We propose a method for the determination of magnetic monopole currents in non-Abelian gauge theories which does not need a projection to Abelian degrees of freedom. With this definition we are able to determine the distribution of magnetic currents and electric fields for the gluonic flux tube between a pair of static charges. Further we check the validity of the Gauss law and the dual London equation in a gauge invariant formulation.

In the Abelian dual Higgs model with dual Dirac strings suggested by Faber et al. [Nucl. Phys. B 475 (1996) 73] the quantum fluctuations of the dual-vector and the Higgs fields around an Abrikosov flux line are taken into account in one-loop approximation. The contribution to the string energy induced by such fluctuations is computed. An important role of quantum fluctuations for the formation of a linearly rising interquark potential is claimed.

We study the phase structure of full QCD within the canonical ensemble with respect to triality in a lattice formulation. The procedure for the calculation of the effective potentials in this case is given. As an example we consider the three dimensional SU(2) gauge model at finite temperatures in the strong coupling region. The potential exhibits a deconfinement phase transition unlike the similar potential obtained in the grand canonical ensemble which demonstrates explicit Z(N) symmetry breaking at any temperature. Furthermore, we investigate the effective potential with the chiral condensate included. In contradiction to other authors, we find chiral symmetry restoration in all triality sectors. In the scheme with massless staggered fermions we observe chiral symmetry restoration accompanying a deconfinement phase transition of first order. Above the critical point, besides two Z(2) symmetric "deconfining" vacua there exists a metastable "confining" vacuum in a wide region of parameters. Such a picture could be interpreted as an indication on a mixed state of hadrons and quarks in the vicinity of the critical line., Comment: 17 pages with 6 eps. figures included

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.

The present status of the nuclear reaction rates determining the solar neutrino flux is discussed. This includes the reaction rates for the two branching ratios of the three pp-chains involving the reactions 3He(3He,2p)4He and 3He(4He,γ)7Be for the first branching, and 7Be(e−, νe)7Li and 7Be(p, γ)8B for the second branching. Mainly we will concentrate on the basic nuclear reaction p + p → D + e+ + νe of the pp-chains. This reaction rate can only be determined using the theoretical methods. The present status of the application of the relativistic field theory model of the deuteron for this reaction will be discussed.

At large separations static color sources of non-vanishing N-ality give rise to gluonic flux tubes and a linearly rising potential. This behavior is caused by the non-perturbative QCD-vacuum which compresses the gluonic flux. Center vortices [1, 2],quantized magnetic flux lines, play an important role for the confinement of color charges, as has been shown by numerical calculations[3]. In addition, simulations have indicated that vortices could also account for phenomena related to chiral symmetry, such as topological charge and spontaneous chiral symmetry breaking (SCSB) [4, 5]. It is well-known that these non-perturbative features of QCD are intimately linked to the properties of the low-lying spectrum of the Dirac operator. The topological charge of a gauge field equals the index of the Dirac operator, while the chiral condensate, the order parameter for SCSB, is proportional to the spectral density of the near-zero modes. With the advent of the overlap operator [6, 7], the fundamental problems of investigating chiral features on the lattice have been overcome. The overlap operator has an exact chiral symmetry [8], implements a lattice version of the index theorem [6], and may even be used for the definition of a local topological charge density [4]. We work with SU(2) gauge fields on lattices with Ns sites in the x-, yand z-direction, and Nt sites in the t-direction. In four dimensions vortices form closed two-dimensional surfaces. We investigate thick classical center vortices in the shapes of planes (closed by lattice periodicity) and spheres. The details of the individual vortex types will be discussed along with our results. We report on our calculations with the overlap operator applied to thick classical center vortices. We investigate the localization of zero-modes with respect to the position of the thick vortices and find an interesting discrepancy in the topological charge determined by different methods.

We propose a model of monopoles where a condensate of monopole-antimonopole pairs leads to confinement. We investigate the condensation of these monopole-antimonopole pairs around a dual Dirac string.

We investigate a dual Higgs model with dual Dirac strings invariant under U (1) gauge transformations, where U (1) is the Abelian gauge group of dual-vector potential transformations spontaneously broken by the Higgs mechanism. The action of a dual Dirac string calculated in leading order in the large Higgs field mass expansion coincides with a dual version of that obtained by Nambu. For the example of the string tension at the classical tree-level approach we develop a procedure for the computation of contributions of string-string interactions. Non-perturbative phenomena of compact QED are discussed.