Linear Gauge Research Articles

Symmetric point four-point functions at one loop in QCD

We evaluate the quartic ghost and quark Green's functions as well as the gluon-ghost, gluon-quark and ghost-quark four-point functions of quantum chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green's functions in quantum electrodynamics are also provided.

Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST-invariant two-point correlation function

In order to construct a gauge invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge invariant transverse configurations A^h. Such configurations can be obtained through the minimization of the functional A^2_{min} along the gauge orbit within the BRST invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of non-perturbative aspects of the theory in a BRST invariant and gauge parameter independent way. In particular, it turns out that the poles of <A^h A^h> are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST invariant formulation introduced before. Moreover, the correlator <A^h A^h> enables us to attach a BRST invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of <A^h A^h> as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use <A^h A^h> to probe the pole structure of the massive gauge boson in a gauge invariant fashion.

Schwinger mechanism in linear covariant gauges

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\"atze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ans\"atze are compatible with the existence of nontrivial solutions. When such Ans\"atze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing", while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.

Gauge coupling field, currents, anomalies and [formula omitted] super-Yang–Mills effective actions

Working with a gauge coupling field in a linear superfield, we construct effective Lagrangians for N=1 super-Yang–Mills theory fully compatible with the expected all-order behavior or physical quantities. Using the one-loop dependence on its ultraviolet cutoff and anomaly matching or cancellation of R and dilatation anomalies, we obtain the Wilsonian effective Lagrangian. With similar anomaly matching or cancellation methods, we derive the effective action for gaugino condensates, as a function of the real coupling field. Both effective actions lead to a derivation of the NSVZ β function from algebraic arguments only. The extension of results to N=2 theories or to matter systems is briefly considered. The main tool for the discussion of anomalies is a generic supercurrent structure with 16B+16F operators (the S multiplet), which we derive using superspace identities and field equations for a fully general gauge theory Lagrangian with the linear gauge coupling superfield, and with various U(1)R currents. As a byproduct, we show under which conditions the S multiplet can be improved to contain the Callan–Coleman–Jackiw energy-momentum tensor whose trace measures the breaking of scale invariance.

The Gribov Horizon in Linear Gauges

The form of the Gribov horizon functional in a linear gauge in the Gribov–Zwanziger theory is discussed.

Diagrammatic cancellations and the gauge dependence of QED

This letter examines diagrammatic cancellations for Quantum Electrodynamics (QED) in the general linear gauge. These cancellations combine Feynman graphs of various topologies and provide a method to reconstruct the gauge dependence of the electron propagator from the result of a particular gauge by means of a linear Dyson-Schwinger equation. We use this method in combination with dimensional regularization to demonstrate how the 3-loop ${\epsilon}$-expansion in the Feynman gauge determines the ${\epsilon}$-expansions for all gauge parameter dependent terms to 4 loops.

Impacts of Contracted Endodontic Cavities on Instrumentation Efficacy and Biomechanical Responses in Maxillary Molars

IntroductionRecently, we reported that in mandibular molars contracted endodontic cavities (CECs) improved fracture strength compared with traditional endodontic cavities (TECs) but compromised instrumentation efficacy in distal canals. This study assessed the impacts of CECs on instrumentation efficacy and axial strain responses in maxillary molars. MethodsEighteen extracted intact maxillary molars were imaged with micro–computed tomographic imaging (12-μm voxel), assigned to CEC or TEC groups (n = 9/group), and accessed accordingly. Canals were instrumented (V-Taper2H; SSWhite Dental, Lakewood, NJ) with 2.5% sodium hypochlorite irrigation, reimaged, and the proportion of the modified canal wall determined. Cavities were restored with bonded composite resin (TPH-Spectra-LV; Dentsply International, York, PA). Another 28 similar molars (n = 14/group) with linear strain gauges (Showa Measuring Instruments, Tokyo, Japan) attached to mesiobuccal and palatal roots were subjected to load cycles (50–150 N) in the Instron Universal Testing machine (Instron, Canton, MA), and the axial microstrain was recorded before access and after restoration. These 28 molars and additional 11 intact molars (control) were cyclically fatigued (1 million cycles, 5–50 N, 15 Hz) and subsequently loaded to failure. Data were analyzed by the Wilcoxon rank sum and Kruskal-Wallis tests (α = 0.05). ResultsThe overall mean proportion of the modified canal wall did not differ significantly between CECs (49.7% ± 12.0%) and TECs (44.7% ± 9.0%). Relative changes in axial microstrain responses to load varied in both groups. The mean load at failure for CECs (1703 ± 558 N) did not differ significantly from TECs (1384 ± 377 N) and was significantly lower (P < .005) for both groups compared with intact molars (2457 ± 941 N). ConclusionsIn maxillary molars tested in vitro, CECs did not impact instrumentation efficacy and biomechanical responses compared with TECs.

Aspects of the refined Gribov–Zwanziger action in linear covariant gauges

We prove the renormalizability to all orders of a refined Gribov–Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev–Popov operator is positive definite with respect to the transverse component of the gauge field, a procedure which turns out to be analogous to the restriction to the Gribov region in the Landau gauge. The model studied here can be regarded as the first approximation of a more general nonperturbative BRST invariant formulation of the refined Gribov–Zwanziger action in linear covariant gauges obtained recently in Carpi et al. (2015, 0000). A key ingredient of the set up worked out in Carpi et al. (2015, 0000) is the introduction of a gauge invariant field configuration Aμ which can be expressed as an infinite non-local series in the starting gauge field Aμ. In the present case, we consider the approximation in which only the first term of the series representing Aμ is considered, corresponding to a pure transverse gauge field. The all order renormalizability of the resulting action gives thus a strong evidence of the renormalizability of the aforementioned more general nonperturbative BRST invariant formulation of the Gribov horizon in linear covariant gauges.

Vortices and Vermas

In three-dimensional gauge theories, monopole operators create and destroy vortices. We explore this idea in the context of 3d N=4 gauge theories in the presence of an Ω-background. In this case, monopole operators generate a non-commutative algebra that quantizes the Coulomb-branch chiral ring. The monopole operators act naturally on a Hilbert space, which is realized concretely as the equivariant cohomology of a moduli space of vortices. The action furnishes the space with the structure of a Verma module for the Coulomb-branch algebra. This leads to a new mathematical definition of the Coulomb-branch algebra itself, related to that of Braverman–Finkelberg–Nakajima. By introducing additional boundary conditions, we find a construction of vortex partition functions of 2d N=(2,2) theories as overlaps of coherent states (Whittaker vectors) for Coulomb-branch algebras, generalizing work of Braverman–Feigin–Finkelberg–Rybnikov on a finite version of the AGT correspondence. In the case of 3d linear quiver gauge theories, we use brane constructions to exhibit vortex moduli spaces as handsaw quiver varieties, and realize monopole operators as interfaces between handsaw-quiver quantum mechanics, generalizing work of Nakajima.

Unified description of seagull cancellations and infrared finiteness of gluon propagators

We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of 'seagull cancellations' among the one- and two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared.

Local and BRST-invariant Yang-Mills theory within the Gribov horizon

We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter itxndependence of all correlation functions of local BRST-invariant operators.

Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space

We construct the graviton two-point function for a two-parameter family of linear covariant gauges in n-dimensional de Sitter space. The construction is performed via the mode-sum method in the Bunch-Davies vacuum in the Poincar\'e patch, and a Fierz-Pauli mass term is introduced to regularize the infrared (IR) divergences. The resulting two-point function is de Sitter-invariant, and free of IR divergences in the massless limit (for a certain range of parameters) though analytic continuation with respect to the mass for the pure-gauge sector of the two-point function is necessary for this result. This general result agrees with the propagator obtained by analytic continuation from the sphere [Phys. Rev. D 34, 3670 (1986); Class. Quant. Grav. 18, 4317 (2001)]. However, if one starts with strictly zero mass theory, the IR divergences are absent only for a specific value of one of the two parameters, with the other parameter left generic. These findings agree with recent calculations in the Landau (exact) gauge [J. Math. Phys. 53, 122502 (2012)], where IR divergences do appear in the spin-two (tensor) part of the two-point function. However, we find the strength (including the sign) of the IR divergence to be different from the one found in this reference.

METHOD FOR DETERMINATION OF ROTATION CENTER IN VIBRATING OBJECT

Linear piezoelectric gauges, eddy current transducers and other control and measuring devices have been widely applied for vibration diagnostics of objects in industry. Methods based on such gauges and used for measuring angular and linear vibrations do not provide the possibility to assess a rotation center or point angle of an object. Parasitic oscillations may occur during rotor rotation and in some cases the oscillations are caused by dis-balance. The known methods for measuring angular and linear vibrations make it possible to detect the phenomenon and they do not provide information for balancing of the given object. For this very reason the paper describes a method for obtaining instantaneous rotation center in the vibrating object. It allows to improve informational content of the measurements owing to obtaining additional data on position of object rotation center. The obtained data can be used for balancing of a control object. Essence of the given method is shown by an example of piezoelectric gauges of linear vibrations. Two three-axial gauges are fixed to the investigated object. Then gauge output signals are recalculated in angular vibrations of the object (for this purpose it is necessary to know a distance between gauges). Further projection positions of the object rotation center are determined on three orthogonal planes. Instantaneous rotation center is calculated according to the position of one of the gauges. The proposed method permits to obtain data on linear and angular vibrations and rotation center position of the vibrating object using one system of linear gauge. Possibilities of object diagnostics are expanded due to increase in number of determined parameters pertaining to object moving. The method also makes it possible to reduce material and time expenses for measurement of an angular vibration component.

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

Modeling and Development of a Flexible Carbon Black-Based Capacitive Strain Sensor

The wide range of applications of strain sensors leads to an increased interest on flexible, cost effective, and low-power devices for strain and bending measurements. A simply structured sensor that meets these requirements is studied using a finite-element analysis. The sensor design focuses on the sensor performance variations for different applications and takes into account the fabrication process that can be used for elastomeric flexible sensors. Both large and small strain performance is considered. The simulation results are also compared with experimental measurements exploiting a flexible parallel plate capacitive strain sensor comprising carbon black-polydimethylsiloxane (PDMS) composite layers as electrodes and PDMS as the dielectric and encapsulation material. A simple and low-cost fabrication process was used, and the sensor was tested in a cantilever beam measurement setup. The device exhibits linear capacitive response ( $R^{2}=0.999$ ) and gauge factor 1.45 for small strain changes.

Use of Supplemental Short Pre-Contoured Accessory Rods and Cobalt Chrome Alloy Posterior Rods Reduces Primary Rod Strain and Range of Motion Across the Pedicle Subtraction Osteotomy Level

In vitro cadaveric biomechanical study. To assess effects of 4-rod reconstruction, rod material, and anterior column support on motion and surface rod strain in a pedicle subtraction osteotomy model. Pedicle subtraction osteotomy (PSO) can correct significant sagittal deformity of the lumbar spine; however, revision rates are high. To reduce rod strain and the incidence of rod fracture, clinical use of multi-rod construction, cobalt chrome (CoCr) alloy rods, and interbody spacers adjacent to PSO has been proposed. Investigating both motion and rod strain is necessary to determine the biomechanical efficacy of these techniques. Five specimens (T12-S1) underwent PSO at L3 with pedicle screw stabilization at L1-S1. Pedicle subtraction was adjusted to achieve a final lordosis of 70°. Flexion-extension (FE), lateral bending, and axial rotation were applied. Linear strain gauges measured surface rod strain during FE on primary and accessory rods at PSO level. Testing evaluated (1) accessory rods (4-Rod) added at PSO level versus primary rods (2-Rod); (2) Ti versus CoCr rods; and (3) lateral interbody spacers (S) inserted adjacent to PSO. One-way and three-way analysis of variance was performed (P ≤ 0.05). All constructs significantly reduced FE and lateral bending motion relative to intact (P < 0.001). The main effect of accessory rods in reducing FE motion was significant (P = 0.021). Accessory and CoCr rods reduced relative surface strain on the primary rod, irrespective of construct (P < 0.001). CoCr 4-Rod + S provided the greatest reduction in strain (76% decrease; P = 0.003). Accessory and CoCr rods provided greatest reduction in motion and rod strain at PSO level. Interbody devices minimally affected motion-induced strain and might act primarily to maintain disc height. Clinicians must assess whether surface strain and motion reduction minimize the incidence of rod fracture. N/A.

More on the nonperturbative Gribov-Zwanziger quantization of linear covariant gauges

In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.

Six dimensional QCD at two loops

We construct the six dimensional Quantum Chromodynamics (QCD) Lagrangian in a linear covariant gauge and subsequently renormalize it at two loops in the MSbar scheme. The coupling constant corresponding to the gauge interaction is asymptotically free for all numbers of quark fields, Nf. Analysing the beta-functions yields a rich spectrum of fixed points. For instance, the conformal window in the six dimensional theory is at Nf = 16 for the SU(3) colour group. The critical theory structure is similar to that of an O(N) scalar theory in eight dimensions. Using the large N expansion the latter is shown to be in the same universality class as the Heisenberg ferromagnet. Similarly using the large Nf expansion, six dimensional QCD is shown to be in the same class as the two dimensional non-abelian Thirring model and four dimensional QCD. Abelian gauge theories are also renormalized at high loops in six and eight dimensions. It is shown that the gauge parameter only appears in the electron anomalous dimension at one loop, similar to four dimensions.

Characterization of FRP Uwrap Anchors for Externally Bonded FRP-Reinforced Concrete Elements: An Experimental Study

AbstractWhile the majority of U-shape wrapping (Uwrap) studies have focused on the mechanism of the shear-strengthening effect, very few studies have been devoted to the use of Uwraps as anchorage for longitudinal fiber-reinforced polymer (FRP) sheets or plates. This investigation therefore focuses on the anchor effect of the carbon-fiber-reinforced polymer (CFRP) Uwrap on externally bonded FRP-reinforced concrete elements. Based on selected parameters from the preliminary study, a parametric study was conducted on concrete blocks with an attached FRP sheet with and without Uwraps. Pull-out tests were conducted on these specimens. Slips along the length of the FRP sheet and debonding propagation in the region under the Uwrap were observed using a linear variable differential transformer (LVDT) and strain gauges. Among the tested specimens, the FRP Uwraps with a 45° angle without an edge distance maximizes the benefit of the anchoring effect. Two factors were found to control the Uwrap performance: the str...

Strains around distally inclined implants retaining mandibular overdentures with Locator attachments: an in vitro study.

PURPOSEThe aim of the present study was to evaluate, by means of strain gauge analysis, the effect of different implant angulations on strains around two implants retaining mandibular overdenture with Locator attachments.MATERIALS AND METHODSFour duplicate mandibular acrylic models were constructed. Two implants were inserted in the canine regions using the following degrees of distal inclinations: group I (control); 0°, group II; 10°, group III; 20°, and group IV; 30°. Locator pink attachments were used to connect the overdenture to the implants and Locator red (designed for severely angled implants) was used for group IV (group IVred). For each group, two linear strain gauges were attached at the mesial and distal surfaces of the acrylic resin around each implant. Peri-implant strain was measured on loading and non-loading sides during bilateral and unilateral loading.RESULTSFor all groups, the mesial surfaces of the implants at loading and non-loading sides experienced compressive (negative) strains, while the distal implant surfaces showed tensile (positive) strains. Group IV showed the highest strain, followed by group III, group II. Both group I and group IVred showed the lowest strain. The strain gauges at the mesial surface of the loading side recorded the highest strain, and the distal surface at non-loading side showed the lowest strain. Unilateral loading recorded significantly higher strain than bilateral loading.CONCLUSIONPeri-implant strains around two implants used to retain mandibular overdentures with Locator attachments increase as distal implant inclination increases, except when red nylon inserts were used.