Center Symmetry Research Articles

Congruency class effects in the Hosotani model

We examine the Wilson loop breaking of gauge and central symmetries by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions on manifolds of the formR m × S 1 . By writing the effective potential in terms of the polylogarithm function, it is found that the algebra preserving minima are always turning points of the potential and that the positions of the global minima of the potential are independent of the dimension of the space. A condition is obtained for stability of the classical symmetric vacua with respect to radiative corrections. We find that the gauge algebra can only be broken if we have periodic fermions in a representation of the group which lies in the same congruency class as the adjoint representation. The degree of breaking of the covering group central symmetries is found to depend both on the choice of congruency class and boundary condition for the fermion fields.

Magnetic detection for underground pipes (abstract)

Magnetic detection has been investigated for use in detecting the location of underground pipelines, such as gas and water lines, by inputting a signal current into a pipeline and detecting magnetic field (≲100 μG) generated by that current. Measurement factors necessary for accurate detection have been experimentally determined and are discussed. From measurements made on signal current distribution (the current flowing in pipes and leaking from them to ground), it has been concluded that detection error is caused by the leakage current, namely, the current to ground. The detection error is due to the noncenter symmetric distribution of the ground current flowing around a pipe. Even though the ground current is inevitable when flowing a signal current into pipes, it is possible to reduce the error by reducing the nonsymmetry by lowering the signal frequency below 10 kHz in this work. The ground current distribution was obtained by measuring the potential difference between two electrodes, both of which were rod shaped and inserted in the ground to the same depth. At low frequencies below 10 kHz, the ground current distribution in a cross section perpendicular to the pipe showed a rather center symmetry around the pipe, while at high frequencies the distribution changed to a noncenter symmetry with a significant current increase in a region near the ground surface. The drastic change in the distribution of the ground current was also confirmed by magnetic field distribution measurements conducted on the ground using three orthogonally arranged magnetic sensors, each with a sensitivity of 1 μG.

Twisted boundary conditions for gauge theories on a torus

Gauge theories on the torus T2 and higher-dimensional tori are considered. The compactness of these manifolds induces boundary conditions on path integrals, one for each compactified dimension. Gauge fixing affects these boundary conditions, causing them to be nonperiodic in certain gauges, the nonperiodicity being expressed in terms of a gauge transformation or ‘‘twist.’’ The eigenvalues of the twist functions can be interpreted as spin variables in an effective spin theory, as is done in temperature field theory. The spin theory action, the effective potential, center symmetry, and the high-temperature limit are discussed. We clarify the connection between this spin theory and t’Hooft’s formalism for gauge theories on a torus.

Strain-modulated ESR study ofPt−in silicon

Early electron-spin-resonance (ESR) studies by Woodbury and Ludwig on the Pt acceptor in Si have been refined and extended. The strain dependence of the spectroscopic splitting tensor $\stackrel{\ensuremath{\leftrightarrow}}{\mathrm{g}}$ has been measured using the strain-modulated electron-spin-resonance technique. The symmetry of the center proves to be monoclinic. The 20 independent elements of the magnetoelastic tensor $\stackrel{\ensuremath{\leftrightarrow}}{\mathrm{F}}$ allowed in ${C}_{s}$ symmetry are determined at $T=4.2$ K. New details in the ESR spectra are also reported. A superhyperfine structure due to a second Pt atom indicates that Pt enters the lattice as pairs. Experiments on samples with varying Pt and P concentrations show that in the concentration range ${10}^{16}$ [Pt] ${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, Pt is exclusively present as ${\mathrm{Pt}}^{\ensuremath{-}}$${\ensuremath{-}\mathrm{P}\mathrm{t}}^{0}$ pairs. Single ${\mathrm{Pt}}^{\ensuremath{-}}$ centers are not observed. The doubly charged pair state ${\mathrm{Pt}}^{\ensuremath{-}}$${\ensuremath{-}\mathrm{P}\mathrm{t}}^{\ensuremath{-}}$ is also absent, even in samples with high [P]/[Pt] ratio. This implies that both members of the pair must be located at distinct types of sites. The following model accounts for all observed features: One of the platinums (${\mathrm{Pt}}^{\ensuremath{-}}$) is at a near-substitutional site. It forms chemical bonds with two neighboring silicon atoms and is shifted in their direction along a [001] axis. The remaining two silicon neighbors form a reconstructed bond. The second ${\mathrm{Pt}}^{0}$ atom is at an interstitial site; its presence is responsible for the monoclinic (${C}_{s}$) center symmetry.

Critical behavior at finite-temperature confinement transitions

Confinement in a pure gauge theory at non-zero temperature may be discussed in terms of an order parameter which transforms under a global symmetry group, the center of the gauge group. Integrating out all degrees of freedom except this order parameter generates an effective scalar field theory for the order parameter, globally invariant under the center symmetry. We argue that the effective theory possesses only short-range couplings, and hence that the finite-temperature confinement phase transition (when continuous) is accompanied by long-range fluctuations only in the order parameter. Universality ideas then lead to predictions for the critical properties of U(1), Z( N), and SU( N) gauge theories for all dimensionalities of space-time. An explicit renormalization-group calculation is presented for the U(1) gauge theory in (2 + 1) dimensions, the results of which fit the general picture.

Interaction induced light scattering in orientationally disordered crystals: the translational phonon region

We have derived an expression for the light scattering spectrum of a crystal in which the mechanically regular sites are occupied by point polarizable orientationally disordered molecules when the polarizabilities are assumed to depend on the positions of the surrounding atoms (interaction induced polarizability fluctuations). Owing to the ‘electrical’ disorder properties of the system all phonons can contribute to the anisotropic scattering measured in all polarization configuration with wavevector, branch index and polarization dependent coefficients. Assuming short range interaction induced polarizabilities we show that the temperature reduced intensity I(ω)/[n(ω) + 1] is given by a superposition of the Brillouin zone centre symmetry ‘projected’ density of states with polarization dependent coefficients. These coefficients are found to be essentially frequency independent for all the projections, exception made for those corresponding to the acoustic phonons. For the acoustic branches the coefficients vanish in a first approximation. They can however be treated on more rigorous grounds and, as already found by other authors, their contribution is proportional to the density of states multiplied by ω2. In addition zone centre (k⋍0) totally symmetric phonons can also be present in the ‘isotropic’ term (which appears only in the polarized VV configuration). A procedure is suggested to obtain the total density of states from the spectra measured in different polarization configurations.

Phase transition over the gauge group center and quark confinement in QCD

A lattice gauge model with the phase transition corresponding to spontaneous breakdown of the group center symmetry is considered. The possible continuum limit in a phase with permanently confined quarks is discussed.

On the problem of the reproduction of the true orientation distribution from pole figures

It recently became evident that the Bunge-method of calculation for the orientation distribution function (ODF) from pole figures did not yield satisfactory approximations of the true ODF. The obtained ODF's show the correct positions of strong maxima indeed, however, contain erroneous fluctuations which suggest nonexistent maxima (ghosts). Since it is in principle not possible to reproduce the ‘true’ ODF from pole figure data (because of its centre symmetry) it is suggested to overcome these falsifications with the help of additional model type suppositions. In this paper some observations of ghosts in experimental ODF's will be discussed as well as possibilities to eliminate the ghosts.

Continuous models of transportation and location revisited

It is clear where one can go from here: production of commodities from resources that are either localized (land and immobile labor) or mobile (capital, intermediate goods, and mobile labor) may be introduced explicitly; and special cases may be solved such as the von Thünen economy with one distinguished center and radial symmetry of all activities with respect to that center; or a Launhardt-Lösch economy with a set of market centers serving hexagonal (or differently shaped) market areas. In this way the continuous flow analysis may be firmly embedded in both classical and modern location theory.

Pseudocubic Angular Dependence of the M = − 1/2 to + 1/2 EPR Transitions for Ions with S = 3/2 Produced by Small Crystal Fields of Arbitrary Symmetry and Random Strains

AbstractPrevious investigations of the angular dependence of the −1/2 ⟷ +1/2 transition which turned out to be pseudocubic in spite of lower centre symmetry are extended to the case of arbitrary symmetry. Moreover the influence of random strains is calculated. The result is that also in both these cases the centre of gravity of the line groups exhibits a cubic angular dependence. Thus in the case of unresolved structures and non‐detectable ± 1/2 ⟷ ± 3/2 transitions the exact symmetry of the centre cannot be directly deduced from the angular dependence. The contributions from the local lattice distortions to the cubic angular dependence vary essentially inversely with the square of the magnetic field and can be determined by measuring at different microwave frequencies.

On the structure of finite collineation groups containing symmetries of generalized quadrangles

In this paper we begin to investigate the structure of a generalized quadrangle (~, ~2) which admits a finite collineation group G containing non-identity symmetries. Of course, when starting such an investigation, it is natural to concentrate attention on those cases where G is assumed to satisfy certain irreducibility criteria. The nature of these possible restrictions on the action of G is suggested by examining the substructures of (~, ~). This is done in Section 2. In Section 4 we consider what can be said about the composition series for G. Under relatively weak irreducibility conditions reasonably detailed information is obtained. This is contained in Theorem (4.1). These results are then used in the final section of this article to tackle the problem when both non-trivial axial and central symmetries are present in G. This places surprisingly severe restrictions on the geometry and, consequently, our strongest result is obtained here as (5.1). As a corollary to this theorem we obtain the following characterization:

ENDOR of the FA(Li) Center in KBr at Liquid He Temperatures

The ENDOR of the first-shell of the F A (Li) center in KBr has been measured at 4.2 and 1.8 K. Isotropic and anisotropic h f , and quadrupole interaction constant are tabulated, The Li + ion is sited on the center symmetry axis. The electron density-center is shifted from the center of the anion vacancy to the K + ion site along the symmetry axis.

EPR studies of nitric oxide complexes of turnip and horseradish peroxidases

Electron paramagnetic resonance studies of ferrous nitric oxide complexes of turnip isoperoxidases have shown that the proteic ligand of the heme iron is always a nitrogen atom and that the paramagnetic center symmetry is rhombic. The addition of indoleacetic acid to nitrosyl ferrous peroxidases produced in some cases drastic spectral changes. Indoleacetic acid does not displace nitric oxide, but an interaction does take place between the nitric oxide heme complex and the substrate binding site. Another interaction with a proton binding site is also suggested in the case of horseradish peroxidase.

Electron paramagnetic studies of nitric oxide haemoglobin derivatives: Isolated subunits and nitric oxide hybrids

The electron paramagnetic resonance spectra of various nitrosyl-haemoproteins have been studied at room temperature and at 77 °K. A detailed investigation of the isolated α NO, β NO> and γ NO chains of human haemoglobins has led to the description of new spectral features. These are tentatively assigned in terms of paramagnetic centre symmetry and of the hyperfine interactions of unpaired electrons with the nitrogen nuclei of the proximal histidine and the liganded nitric oxide. Furthermore, electron paramagnetic resonance spectra are described for various haemoglobin nitric oxide hybrids in which one type of chain is liganded to NO and the partner chain can take a variety of ligation and valency states, namely ferrous (deoxy, oxy and carboxy) or ferric (aquo, fluoride, azide and cyanide). The electron paramagnetic resonance spectra at 20 °C and 77 °K of the α NO β hybrids are found to depend on the spin state of the haem carried by the β chain: for low spin, the spectra are identical to those of the free α NO subunit; for high spin, the spectra are modified. Such modifications are generally assigned to an alteration of the d z2 — σ∗ molecular orbital containing the unpaired electron. By contrast, the electron paramagnetic resonance spectra of the αβ NO hybrids were always identical to those of the isolated β NO subunits, independently of the spin state of the α haem. The results are discussed in the light of the subunit non-equivalence and of the importance of the haem spin state changes in the mechanism of haem-haem interaction.

Formation kinetic study of aggregate color centers with zero-phonon lines in NaF

Abstract Formation kinetic measurements for a number of F aggregate color centers in NaF were performed using the zero-phonon absorption lines 5456 A, 5754 A, and 6070 A as well as the F, M , and R 2 absorption bands. Taking into account the color center symmetries obtained from uniaxial stress experiments several possible models for the centers which give rise to the zero-phonon lines are discussed.

Local Vibrations of Divalent and Univalent Complex Ions in KCl Crystals

AbstractA study has been made of the infrared absorption spectra of KCl crystals containing as impurities complex ions NO, CO, and SO, as well as divalent metals Ca2+, Sr2+, Cu2+. A dependence was found of the complex ion local vibration spectra on the ionic charge. The degenerate vibrations of the divalent ions CO and SO in a crystal were shown to split whereas in the case of the univalent ions NO3 in the crystal the corresponding vibrations remained degenerate. The splitting of degenerate vibrations in the case of divalent ions is attributed to a lowering of the impurity centre symmetry resulting from a formation of complexes with anion vacancies or divalent metals.

Stress effects on 9 572 cm −1 line in irradiated MgO

Piezospectroscopic analysis of the 9 572 cm −1 zero-phonon line in neutron-irradiated MgO yields rhombic I center symmetry. Stress data are used to calculate the associated one-phonon spectrum in the Debye region in good agreement with spectroscopic observations.

The Group Generated by Central Symmetries, with Application to Polygons

The Group Generated by Central Symmetries, with Application to Polygons

The Group Generated by Central Symmetries, with Application to Polygons

The Group Generated by Central Symmetries, with Application to Polygons