Gauge Operators Research Articles

Gluon propagator in non-Abelian Weizsäcker-Williams fields

We carefully compute the gluon propagator in the background of a non--Abelian Weizs\"{a}cker--Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well known problem of the Hermiticity of certain operators in Light Cone gauge is resolved for the Weizs\"{a}cker--Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are absent and then gauge transforming the small fluctuation fields to Light Cone gauge.

INFINITESIMAL GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS

This paper derives explicit expressions of the infinitesimal gauge operators for pseudoscalalr fields in a gauge theory coupling vector and axial-vector fields with the aid of the method of operator algebra. The gauge operators of the coset pure gauge fields theory under the chiral group SU(N) × SU(N) are also obtainede.

In situ neutral pressure measurements in a compact high-field tokamak, Alcator C-Mod

The Alcator C-Mod advanced divertor program requires fast in situ, absolutely calibrated neutral pressure measurements. The concept of a linear-geometry ionization gauge, first implemented at Princeton and Garching, was further developed at the MIT Plasma Fusion Center, to meet Alcator C-Mod requirements (high field, compact design). In order to correctly interpret experimental data, the gauge was subjected to a series of in situ calibration tests. It has been found that the gauge sensitivity increases with increasing parallel (to gauge axis) magnetic field. In the high-pressure, high-field limit the basic assumption of the operation of ionization gauges, Ii/Ie≪1, no longer holds. Consequently a modified expression for the gauge sensitivity, which is a strong function of the primary electron current, is necessary to linearize gauge response over a broad pressure range. Representative pressure measurements from the Alcator C-Mod divertor are included.

Remarks on dispersionless KP, KdV, and 2D gravity

We use the SDiff(2) framework of Takasaki and Takebe and the (L, M) program (L is the Lax operator andMω=ωλ) to show that\(\mathfrak{M}\)=semiclassical limit ofM is\(\hat \xi + \sum\nolimits_2^\infty {T'_n } \lambda ^{n - 1} \), where (\(\lambda , - \hat \xi \)) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also show\(\hat \xi \) is the semiclassical limit ofWxW −1 (W is the gauge operator), whereG=WxW −1 is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version of the Jevicki-Yoneya action principle for 2D gravity, where again\(\hat \xi \) arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas.

Correlation decay in low-dimensional spin glasses

A new method to investigate the two-point correlation function decay in a finite size random spin system and at finite temperatures is proposed. It is applicable to systems with cyclic boundary conditions and in any local or uniform magnetic field. The efficiency of this method is presented in the case of an isotropic XY spin glass model with Gaussian bond distribution in external field. Using unitary U(1) gauge transformation and operator inequalities we have obtained explicit upper bounds for generalized spin-glass susceptibility κ(T,R) that describes off-diagonal transverse magnetization in two dimensional random XY spin lattices at finite temperatures. It is found that the slowest possible decay for susceptibility in random XY spin glass is of the Kosterlitz–Thouless-type with power-law decay in 2D, and the exponential type in 1D, at low temperatures. These upper bounds rule out the possibility of the corresponding magnetic ordering in 1D and 2D isotropic XY spin glasses at finite temperatures.

Using Downhole Pressure Gauges in Hostile Deep Wells, Villafortuna-Trecate Field

This paper summarizes extensive, pioneering experience with the first 5-year well-testing project in the hostile ultradeep wells of the Villafortuna-Trecate field. Performance of the various downhole high-temperature, high-pressure (HTHP) gauges used is investigated, and the relevant technology is compared throughout the field history. Awareness of the quality of data acquired and the role played by redundancy (use of more gauges simultaneously) are identified as key points in planning successful future HTHP operations.

Renormalization of gauge-invariant composite operators in the light-cone gauge.

We generalize to composite operators concepts and techniques which have been successful in proving renormalization of the effective Action in light-cone gauge. Gauge invariant operators can be grouped into classes, closed under renormalization, which is matrix-wise. In spite of the presence of non-local counterterms, an ``effective" dimensional hierarchy still guarantees that any class is endowed with a finite number of elements. The main result we find is that gauge invariant operators under renormalization mix only among themselves, thanks to the very simple structure of Lee-Ward identities in this gauge, contrary to their behaviour in covariant gauges.

Weak matrix elements with gauge invariant Kogut-Susskind operators

Pion decay constant and K meson B parameter are evaluated using non-local operators with and without gauge link variables addressing the question how the choice of operators affect the value of matrix elements. Calculation is made for both full and quenched QCD with Kogut-Susskind fermions. It is shown that the results obtained with the gauge non-invariant operators agree with those of the gauge invariant operators, if corrected by the Z factor using the mean-field improvement of the gauge coupling constant and operators.

Pion decay constant in full lattice QCD

The pion decay constant is calculated for full QCD on the lattice employing a variety of methods derived from current algebra and PCAC relations. The calculation is made at β=5.7 on a 20 4 lattice with two flavors of Kogut-Susskind quarks. Most of the calculation is made in the Landau gauge, for which various methods give results in a very good agreement, yielding ƒ π=97±9 ( statistical) ± 4 ( systematic) MeV . In particular the results obtained with the gauge non-invariant axial-vector current perfectly agrees with those of the gauge invariant current, if corrected by the Z factor using the mean-field improvement of the gauge coupling constant and operators. Dependence of the results on the type of gauge fixing is also examined using the Coulomb gauge.

Intercomparison of hydraulic pressure measurements to 28 MPa using a single-piston gauge in the controlled-clearance, reentrant, and simple configurations

The use of controlled-clearance piston gauges as highly accurate primary pressure standards is well established. However, the operation of a controlled-clearance gauge is more complicated than that of the familiar simple or reentrant designs. An investigation has been performed on a modified design of a piston gauge for which the same piston/cylinder can be operated in either the controlled-clearance, simple, or reentrant modes, to determine the degree of degradation in accuracy of measured pressure using the gauge in either the simple or reentrant modes as a standard. How the particular characterization of the standard gauge affects the calibration parameters of a test gauge is also explored. The effective areas of the test gauge are within 4.5 parts per million (ppm) when the standard is used in the simple mode instead of the controlled-clearance mode, up to a pressure of 28 MPa, whereas in the case of the reentrant mode this deviation increases from 2.5 ppm at 7 MPa to 14 ppm at 26 MPa.

Stochastic Integration on the Full Fock Space with the Help of a Kernel Calculus

We develop a stochastic integration theory with respect to creation, annihilation and gauge operators on the full Fock space. This is done by using a kernel representation for a large class of bounded operators on the full Fock space. It is shown that the kernels form a Banach algebra. Having established the definition of processes and stochastic integrals we go on to prove an Ito formula and use this for examining stochastic evolutions and constructing dilations of special completely positive semigroups. Explicit solutions of the corresponding stochastic differential equations are given.

Generalized Calibration of a Nuclear Moisture/Density Depth Gauge

Abstract The application of nuclear moisture/density depth gauges to soil deposits has generally relied on calibration by direct correlation with measured values of moisture content and density. In very soft variable deposits such as coal tailings, direct calibration is not possible. A generalized calibration can be developed from first principles based on the elemental composition of the soil being tested and the application of existing theories. Density and moisture content calibrations are considered separately for two different access tubes, and reasonably reliable calibrations are obtained. In applying these calibrations, an iterative procedure is required since the moisture content has a direct bearing on the elemental composition of the moist soil. The paper gives an insight into the operation and important features of a nuclear gauge.

Weak interaction matrix elements with staggered fermions

We present a progress report on the calculation of weak interaction matrix element using staggered fermions. We are using several new techniques, including include Landau gauge operators and quark wall propagators. We give preliminary results for the kaon B parameter.

The Gauge Operators for Pseudoscalar Fields and the Baker-Hausdorff Formula

In this paper, we present the explicit expressions of the gauge operators for pseudoscalar fields in a gauge theory coupled vector and axial-vector fields with the aid of the method of operator algebras. The gauge operators of the pure gauge field theory under the chiral group are also presented. Moreover, the explicit expression of the Baker-Hausdorff formula is obtained for a special case and the general situation is discussed.

Laboratory Investigation of Nuclear Density Gauge Operation

ABSTRACT THE introduction of nuclear density gauges has brought with it the potential for fast, easy and accurate soil density measurements. However, before these gauges can be used in the field, their performance must be evaluated. Performance tests were conducted on a Campbell Pacific MC-2 gauge to determine its adequacy for measuring soil wet density. Resolution and factors affecting the operation of the gauge were analyzed. Soil density measured with the gauge correlated well with average box densities in laboratory tests.

The design and operation of a new extractor gauge

A new type of extractor gauge with a cylindrical reflector and a squirrel-cage grid shaped as a frustum of a cone is presented. The trajectories of electrons and ions are evaluated by numerical method, while the extraction and collection efficiency of the new gauge, as well as its x-ray current, have been studied experimentally. These results show that the new geometry with appropriate applied voltage of the gauge are favorable for enhancing the sensitivity and reducing the x-ray current. It has been found that self-modulation and ‘‘deep modulation’’ can be used to determine the x-ray current of an extractor gauge without an additional modulator electrode. An interesting result of deep modulation is that the value of modulation factor k (defined as the ratio of the collector current at modulation to normal operating conditions at high vacuum, 10−6–10−8 Torr) of 10−4 has been achieved, so that the x-ray current can be measured at a pressure 2–3 orders of magnitude higher than the x-ray limit by deep modulation. As a result of this improvement in design and operation of the extractor gauge, both of the x-ray limits estimated by comparing with a normal Bayard–Alpert gauge in geometry factor and measured by using the deep modulation are less than 1×10−13 Torr (equivalent for N2), and the sensitivity is about 25 Torr−1.

Gauging frequency and detection of rating changes

ABSTRACT For gauging stations where rating changes are frequent, errors in streamflow estimation can occur from using out-of-date stage-discharge ratings. The chance of such errors occurring can be reduced by increasing the frequency of flow gaugings. An expression for the confidence in the accuracy of a flow record is derived which depends on the time interval between gaugin The information provided by the analysis can be used to estimate probable errors in existing records and to control future gauging operations. Application of the analysis is illustrated by a comparison of records from seven stations in New Zealand with mean flows from 2 to 200 m3 s−1, and for those records, missed rating changes are the only significant contribution to the probable error of annual flows.

スピニングローター真空計の起動時オフセット圧力変動の解析

Just after starting the operation of a spinning rotor gauge at pressure less than 2 × 10-6 Pa (nitrogen equivalent), its offset pressure changed by 3 × 10-5 Pa from its final value. A simulation using a personal computer, based on a heat exchange by radiation between a rotor and a rotor tube of the gauge, is carried out to reveal the change in the offset pressure. The result of the simulation showed a good agreement with the time chart of the offset pressure measured experimentally. Influence of parameters, such as linear expansion coefficient, density, specific heat, emissivity of the rotor etc., on the time variation is also studied by the simulation.

Unification of interactions and the constraint on charges in fermion-scalar constituent models.

It is shown that the unification of elementary forces in scalar-fermion preon models depends on the normalization condition imposed on the preonic charge operator Q. One can demand that the normalization of Q equals the normalization of hypercolor and color gauge operators. Alternatively one can construct a simple covering gauge group, which in a plausible way leads to different normalization. Unification, at a reasonable scale M (Mapprox.10/sup 15/ to 10/sup 16/ GeV) imposes some conditions on preonic charges, which are not quite the same for both approaches, which were discussed above. The unification follows for a wider range of parameters in a model in which one fermionic preon transforms as a color triplet, and there is a definitive distinction between two classes of scalar-fermion preon models. The drawback of the approach based on the unification group SU(7) is that it introduces a large number of ''exotic'' preons (i.e., those which do not appear in the composites: quarks, leptons, etc., the total number of preons, 64, is also unacceptably large). It also has some difficulty with the magnitudes of the hypercolor scale and the unification scale.

Quantum de Sitter fiber bundle interpretation of hadron extension

A quantized geometrical description of hadron extension is developed based on Drechsler's soldered de Sitter fiber bundle, which possesses as fiber a local four-dimensional Riemannian space of constant curvature characterized by a radius of curvatureR of the order of 1 Fermi. The structural (gauge) group of the bundle is a de Sitter SO(4, 1), which contains all observable transformations (rotations as well as translations). The quantized de Sitter-structured connection of the bundle leads to a set of self-interaction gauge operators that “act back” on the de Sitter bundle by inducing a local curvature, which, in turn, affects a small neighborhood of the adjoining space-time position, leading to the experimentally observed “size” of the hadron. A particular choice for the quantized Lorentz cross section (gauge) is made that leads to the mathematically consistent and experimentally verifiable hadron model, the quantum relativistic rotator. Also investigated is the limit corresponding to taking the radius of curvature of the de Sitter fiber to infinity.