Gauge Mode Research Articles

Pneumatic gauge pressure comparison measurements between the UME (Turkey) and the CMI (Czech Republic) − EUROMET project No. 537

The results are presented of a bilateral comparison of pneumatic pressure measurements, carried out in the framework of EUROMET Project No. 537, between the Cesky Metrologicky Institut (CMI, Czech Republic) and the TÜBITAK-Ulusal Metroloji Enstitüsü (UME, Turkey). The measurements, in the range 15 kPa to 7 MPa, were carried out in two phases: (i) 18-24 June 1999 at the Pressure Section of the CMI in the range 15 kPa to 350 kPa; (ii) 29 June-8 July 1999 at the Pressure Section of the UME in the ranges 0.25 MPa to 1.75 MPa and 1 MPa to 7 MPa. Three different gas-operated reference standards were used. For the ranges 15 kPa to 350 kPa and 0.25 MPa to 1.75 MPa these were piston-cylinder assemblies with ceramic pistons and tungsten-carbide cylinders and nominal effective areas of 10 cm2 and 2 cm2, respectively. For the range 1 MPa to 7 MPa, a piston-cylinder assembly with tungsten-carbide piston and cylinder and a nominal effective area of 0.5 cm2 was used. The purpose of the measurements was to compare the effective areas of the Czech and Turkish primary pressure standards in gas media and gauge mode, and to confirm the agreement between the pressure scales of the two countries in the range 15 kPa to 7 MPa by application of the cross-floating method. Since the UME and the CMI are participating in different loops of EUROMET Project No. 439, a key comparison of pneumatic pressure, another important goal of this study was to establish a cross-link between the two loops.

Gravitational waves in open de Sitter space

We compute the spectrum of primordial gravitational wave perturbations in open de Sitter spacetime. The background spacetime is taken to be the continuation of an O(5) symmetric instanton saddle point of the Euclidean no boundary path integral. The two-point tensor fluctuations are computed directly from the Euclidean path integral. The Euclidean correlator is then analytically continued into the Lorentzian region where it describes the quantum mechanical vacuum fluctuations of the graviton field. Unlike the results of earlier work, the correlator is shown to be unique and well behaved in the infrared. We show that the infrared divergence found in previous calculations is due to the contribution of a discrete gauge mode inadvertently included in the spectrum.

Pressure comparison measurements between the CMI and the PTB in the range 0.07 MPa to 0.4 MPa

This report describes pressure comparison measurements in the range 0.07 MPa to 0.4 MPa between the Czech Institute of Metrology (CMI) and the Physikalisch-Technische Bundesanstalt (PTB) in the period 9 to 13 March 1998 at the Pressure Section of the PTB, Braunschweig. The transfer standard used was a gas-operated piston-cylinder assembly with a ceramic piston of nominal effective area 10 cm2 and a tungsten-carbide cylinder, installed in a pressure balance base unit, model PG 7601, manufactured by DH Instruments, USA. The measurements compare the effective area of the transfer piston-cylinder assembly as determined from dimensional data at the CMI with effective area data obtained from pressure measurements (i) in gauge mode with the primary standard pressure balance and (ii) in absolute and gauge mode with the primary standard dual-cistern mercury manometer of the PTB. Both primary standard instruments have been used in the international comparison measurements organized by the Consultative Committee for Mass and Related Quantites (CCM) of the Comité International des Poids et Mesures. It may be seen that geometrical measurement values of the effective area is minimal: for the standard pressure balance, 3.4 × 10-6 for absolute pressure, 3.4 × 10-6 for gauge pressure; and for the dual-cistern mercury manometer, 1.8 × 10-6 for gauge mode. The relative difference between the experimetnal absolute and gauge mode for the dual-cistern mercury manometer is 1.5 × 10-6.

CCM key comparison in the pressure range 50 kPa to 1000 kPa (gas medium, gauge mode). Phase A2: Pressure measurements

As part of a wide-ranging key comparison organized by the Consultative Committee for Mass and Related Quantities (CCM) of the Comité International des Poids et Mesures, this report gives the results of a comparison of pressure measurements in the range 0.05 MPa to 1 MPa. The two transfer standards used were pressure balances equipped with large (10 cm2) effective area piston-cylinder assemblies. The scope of the comparison covered the observation of the behaviour of both piston and cylinder assemblies from two manufacturers and made from different materials. The results show agreement of all the laboratory standards within the estimated expanded uncertainties, expressed with a coverage factor k = 2. Most of the difference values (47 out of 54) are inside the standard uncertainties. These results demonstrate the coherency of the standards of the participating laboratories in the range 100 kPa to 1000 kPa for gas pressure, gauge mode.

CCM key comparison in the pressure range 0.05 MPa to 1 MPa (gas medium, gauge mode). Phase A1: Dimensional measurements and calculation of effective area

The results obtained by five laboratories in the determination from dimensional measurements of the effective areas of two gas-operated 10 cm2 piston-cylinder assemblies are presented. These measurements were carried out as phase A1 of a key comparison in the pressure range 0.05 MPa to 1 MPa under the auspices of the Consultative Committee for Mass and Related Quantities (CCM) of the Comité International des Poids et Mesures. The participants performed diameter, straightness and roundness measurements on each piston and cylinder bore and calculated the effective area of each piston-cylinder assembly using their own methods. The differences between diameters determined by the institutes are systematic and often greater than the uncertainties claimed by the participants. Nevertheless, all calculated effective areas agree with the reference values determined within the expanded uncertainties with a coverage factor 2, most of them even within their standard uncertainties. The choice of calculation method seems to be less important than the dimensional data themselves. The effective areas determined from the dimensional measurements are compared with those obtained in cross-float experiments with national pressure standards, in a comparison referred to as phase A2 and reported in a separate paper.

New BNM-LNE standard for absolute pressure measurements up to 1 MPa

The main characteristic of the new Bureau National de Metrologie-Laboratoire National d'Essais (BNM-LNE) pressure balance for measurements in absolute mode is an automatic mechanism for loading the masses on the floating element, allowing a stable residual pressure to be maintained during operation. We report the results of a study of fall rate for nitrogen and of pressure stability. With several piston-cylinder assemblies of 10 cm2 and 20 cm2 effective area, cross-floatings have been performed in both gauge and absolute mode using a capacitance diaphragm gauge (CDG) to measure the difference in pressure delivered by each balance. The repeatability of the measurements is less than 0.15 Pa in the range 25 kPa to 200 kPa in both modes.

Final report: Comparison of pressure standards in the range 0.8 MPa to 8 MPa (gas media, gauge mode)

Final report: Comparison of pressure standards in the range 0.8 MPa to 8 MPa (gas media, gauge mode)

Comparison of pressure standards in the range 10 kPa to 140 kPa

This report summarizes the results obtained by twelve laboratories in a comparison of pressure measurement standards in the range 10 kPa to 140 kPa, carried out under the auspices of the Consultative Committee for Mass and Related Quantities. Measurements were taken in the absolute mode and, by some participants, in the gauge mode. Good repeatability and, until near the end, reproducibility were observed in the transfer standard. The results displayed significant differences between some of the participants beyond those expected from their claimed uncertainties.

Pressure comparison in the range from 0.8 to 8 MPa between the UME (Turkey) and the CNR-IMGC (Italy) in gas media and gauge mode

A bilateral study was carried out at the Pressure and Vacuum Laboratory of the UME in cooperation with the CNR-IMGC (Italy) and the UME (Turkey), in October 1996. Two piston-cylinder assemblies were compared by application of the cross-floating method and the comparison was made in the pressure range from 0.8 to 8 MPa in gas media (gauge mode). The IMGC took only one of its piston-cylinder assemblies to the UME which was compared with a UME piston-cylinder assembly. Six measurement cycles were run and forty-two cross-floating equilibrium points were obtained between the two pressure balances. The sensitivity of the cross-floating equilibrium between the two pressure balances ranged from 3.3 to 1 ppm; best sensitivities were obtained at highest pressures. A new value of the effective area of the UME piston-cylinder assembly was derived as a result of this comparison with an uncertainty of 22.3 ppm (2σ level). Considering the previous value of the UME piston-cylinder effective area, this comparison confirmed the agreement of Italian and Turkish pressure scales in gas media from 0.8 to 8 MPa inside the combination of respective declared uncertainties of 11 ppm for the IMGC and 25 ppm for the UME, even at the 1σ level.

レーザ干渉式油マノメータによるゲージ圧力測定

レーザ干渉式油マノメータによるゲージ圧力測定

Zero modes and the vacuum problem: A study of scalar adjoint matter in two-dimensional Yang-Mills theory via light-cone quantization.

SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the light-cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light-cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum mechanical potential governing the dynamical gauge mode. Due to a condensation of the lowest omentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory however, the barrier height appears too small to make any impact in this odel. Although the theory is superrenormalisable on naive powercounting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The open aspects of this problem are discussed in detail.

Towards solving QCD: The transverse zero modes in light-cone quantization.

We formulate QCD in (d+1) dimensions using Dirac's front form with periodic boundary conditions, that is, within Discretized Light-Cone Quantization. The formalism is worked out in detail for SU(2) pure glue theory in (2+1) dimensions which is approximated by restriction to the lowest {\it transverse} momentum gluons. The dimensionally-reduced theory turns out to be SU(2) gauge theory coupled to adjoint scalar matter in (1+1) dimensions. The scalar field is the remnant of the transverse gluon. This field has modes of both non-zero and zero {\it longitudinal} momentum. We categorize the types of zero modes that occur into three classes, dynamical, topological, and constrained, each well known in separate contexts. The equation for the constrained mode is explicitly worked out. The Gauss law is rather simply resolved to extract physical, namely color singlet states. The topological gauge mode is treated according to two alternative scenarios related to the In the one, a spectrum is found consistent with pure SU(2) gluons in (1+1) dimensions. In the other, the gauge mode excitations are estimated and their role in the spectrum with genuine Fock excitations is explored. A color singlet state is given which satisfies Gauss' law. Its invariant mass is estimated and discussed in the physical limit.

Gauge-averaging functionals for Euclidean Maxwell theory in the presence of boundaries

This paper studies the one-loop expansion of the amplitudes of electromagnetism about flat Euclidean backgrounds bounded by a 3-sphere, recently considered in perturbative quantum cosmology, by using -function regularization. For a specific choice of gauge-averaging functional, the contributions to the full value owed to physical degrees of freedom, decoupled gauge mode, coupled gauge modes, and Faddeev--Popov ghost field are derived in detail, and alternative choices for such a functional are also studied. This analysis enables one to get a better understanding of different quantization techniques for gauge fields and gravitation in the presence of boundaries.

Progress Report on an International Intercomparison in the Pressure Range 10 kPa to 140 kPa

Results are summarized from thirteen laboratories which took part in the first four phases of an international intercomparison of pressure measurement standards in the range 10 kPa to 140 kPa, carried out under the auspices of the BIPM. The transfer standard was a gas-operated pressure balance (piston gauge). All participants took measurements in the absolute mode; several also took measurements in the gauge mode. The transfer standard showed good repeatability and long-term stability, and revealed some unexpected and significant differences between some of the participants.

A Review of Gas-operated Piston Gauges

While hydraulic piston gauge technology dates from the mid-1800s, the first practical gas-lubricated pneumatic piston gauges for metrological applications were not developed until almost one hundred years later. The major reason for this delay was the need for adequate materials and machining technology to fabricate pistons and cylinders with tight enough tolerances for acceptable instrument operation. As the need for reduced uncertainties increased for gas pressure measurements in the ranges covered by manometry and above, technological improvement in gas-operated piston gauges advanced rapidly. Requirements for the development of high-quality air bearings added stimulus to the push for improved piston and cylinder technology. Investigations into the possible use of pneumatic piston gauges as primary pressure standards competitive with manometry had begun by 1965. Although lack of a fundamental detailed model of the vertical momentum transfer from the moving gas to the flanks of the piston currently somewhat limits this application, improvements in understanding and technology are continually being made. The relatively recent discoveries of the sometimes significant dependence of the effective area of certain pneumatic piston gauges on the gas species used during operation, or on whether the gauge is operating in the gauge or absolute mode, underscore the need for continued research in this field.

Non-Fermi-liquid behavior in quantum critical systems

The problem of an electron gas interacting via exchanging transverse gauge bosons is studied using the renormalization group method. The long wavelength behavior of the gauge field is shown to be in the Gaussian universality class with a dynamical exponent z=3 in dimensions D\ensuremath{\ge}2. This implies that the gauge coupling constant is exactly marginal. Scattering of the electrons by the gauge mode leads to non-Fermi-liquid behavior in D\ensuremath{\le}3. The asymptotic electron and gauge Green's functions, interaction vertex, specific heat, and resistivity are presented.

Small deformations of the Prasad-Sommerfield solution

I study solutions of the static Euclidean anti-self-dual SU(2) Yang-Mills equations which differ by a small perturbation from the Prasad-Sommerfield solution. I find explicit expressions for two series of perturbation mode functions of angular momentum $l$ and even and odd parity, and classify the modes according to several criteria. There are seven nondilatational modes which have singularities removable by gauge transformation: 3 translations ($l=1$), 1 gauge mode ($l=0$), and a family of 3 odd-parity gauge modes ($l=1$). The translations and $l=0$ gauge modes have nonvanishing, and normalizable, projections into the background gauge, while the odd-parity $l=1$ modes have vanishing projection into the background gauge. Among the singular modes, there are an infinite number of modes, irregular at $r=0$, which nonetheless satisfy the boundary conditions for finite-energy solutions on the sphere at infinity. I show, by discussing the analogous problem of the axially symmetric solutions of the stationary Einstein equations, that non-normalizable modes are relevant in determining whether a spherically symmetric solution of a nonlinear system has axially symmetric extensions. The analysis of perturbations around the Prasad-Sommerfield solution implies that if an axially symmetric extension exists, it cannot be reached by integration out along a tangent vector defined by a nonvanishing, nonsingular small-perturbation mode of the class explicitly constructed.