Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

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—that is, regions whose boundary evaluates to a nontrivial center element—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.

Method of Rotation of Geometrical Objects Around the Curvilinear Axis

Rotation is the motion of geometric objects along a circle. This is one of geometric techniques used to form lines and surfaces. In this paper has been considered the rotation of objects in a three-dimensional space around a straight axis. It is known that a straight line can be considered as a particular case of a circle with a radius equal to infinity. Such circle’s center is at infinite distance from the considered straight line segment. Then in the general case, the rotation axis is a closed curve, for example, a circle with a radius of finite magnitude. Rotation of a point around a straight axis now splits into two trajectories. One of them is a circle with a radius, the second is a straight line crossing with the axis, and the center of this trajectory is at an infinite distance from the point. The method of point rotation about an axis of finite radius was considered. Note that a circle is a special case of an ellipse. When the actual focus of the circle is stratified into two, the line itself loses its curvature constancy, and is called an ellipse. The point, rotating around the elliptical axis, is stratified into four ones, forming four circles (trajectories). Axis foci appearing in turn in the role of the main one determine two trajectories by each with a trivial and nontrivial center of rotation. We have considered the variant for arrangement of the generating circle so that its center coincided with one of the elliptic axis’s foci. The obtained surfaces are a pair of co-axial Dupin cyclides, since they have identical properties. Changing the circle generatrix radius, other things being equal, we get different types of closed cyclides.

Nontrivial center dominance in high temperature QCD

We investigate the properties of quarks and gluons above the chiral phase transition temperature [Formula: see text], using the renormalization group (RG) improved gauge action and the Wilson quark action with two degenerate quarks mainly on a [Formula: see text] lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively [Formula: see text] center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a nontrivial [Formula: see text] center. This is in agreement with our lattice simulation of high temperature quantum chromodynamics (QCD). We further observe that the temporal propagator of massless quarks at extremely high temperature [Formula: see text] remarkably agrees with the temporal propagator of free quarks with the [Formula: see text] twisted boundary condition for [Formula: see text], but differs from that with the [Formula: see text] trivial boundary condition. As we increase the mass of quarks [Formula: see text], we find that the thermal ensemble continues to be dominated by the [Formula: see text] twisted gauge field configurations as long as [Formula: see text] and above that the [Formula: see text] trivial configurations come in. The transition is similar to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks.

GAUGE-EQUIVARIANT HILBERT BIMODULES AND CROSSED PRODUCTS BY ENDOMORPHISMS

C*-endomorphisms arising from superselection structures with nontrivial center define a 'rank' and a 'first Chern class'. Crossed products by such endomorphisms involve the Cuntz–Pimsner algebra of a vector bundle having the above-mentioned rank, first Chern class and can be used to construct a duality for abstract (nonsymmetric) tensor categories versus group bundles acting on (nonsymmetric) Hilbert bimodules. Existence and unicity of the dual object (i.e. the 'gauge' group bundle) are not ensured: we give a description of this phenomenon in terms of a certain moduli space associated with the given endomorphism. The above-mentioned Hilbert bimodules are noncommutative analogs of gauge-equivariant vector bundles in the sense of Nistor–Troitsky.

On the power-commutative kernel of locally nilpotent groups

We define the power-commutative kernel of a group. In particular, we describe the power-commutative kernel of locally nilpotent groups, and of finite groups having a nontrivial center.

DUALITY OF COMPACT GROUPS AND HILBERT C*-SYSTEMS FOR C*-ALGEBRAS WITH A NONTRIVIAL CENTER

In this paper we present duality theory for compact groups in the case when the C*-algebra [Formula: see text], the fixed point algebra of the corresponding Hilbert C*-system [Formula: see text], has a nontrivial center [Formula: see text] and the relative commutant satisfies the minimality condition [Formula: see text] as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*-categories [Formula: see text], where [Formula: see text] is a suitable DR-category and [Formula: see text] a full subcategory of the category of endomorphisms of [Formula: see text]. Both categories have the same objects and the arrows of [Formula: see text] can be generated from the arrows of [Formula: see text] and the center [Formula: see text]. A crucial new element that appears in the present analysis is an abelian group [Formula: see text], which we call the chain group of [Formula: see text], and that can be constructed from certain equivalence relation defined on [Formula: see text], the dual object of [Formula: see text]. The chain group, which is isomorphic to the character group of the center of [Formula: see text], determines the action of irreducible endomorphisms of [Formula: see text] when restricted to [Formula: see text]. Moreover, [Formula: see text] encodes the possibility of defining a symmetry ∊ also for the larger category [Formula: see text] of the previous inclusion.

Superselection Structures for C*-Algebras with Nontrivial Center

We present and prove some results within the framework of Hilbert C*-systems [Formula: see text] with a compact group [Formula: see text]. We assume that the fixed point algebra [Formula: see text] of [Formula: see text] has a nontrivial center [Formula: see text] and its relative commutant w.r.t. ℱ coincides with [Formula: see text], i.e. we have [Formula: see text]. In this context we propose a generalization of the notion of an irreducible endomorphism and study the behaviour of such irreducibles w.r.t. [Formula: see text]. Finally, we give several characterizations of the stabilizer of [Formula: see text].