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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Interpolating the ‘t Hooft model between Instant and Light-Front dynamics in the Coulomb Gauge

The 1+1D model of quantum chromodynamics (QCD) in the infinite number of colors, or 't Hooft model, can be interpolated between the instant form dynamics (IFD) and the light-front dynamics (LFD) using an interpolation parameter 0 (IFD) ≤ δ ≤ π/4 (LFD). This was realized in the interpolating axial gauge which links the axial gauge (A 1 = 0) in IFD and the light-front gauge (A + = 0) [1]. In this presentation, we discuss the corresponding realization in the interpolating Coulomb gauge which links the temporal gauge (A 0 = 0) in IFD and the light-front gauge (A + = 0) and its benefit of resolving the issue associated with the absence of the conjugate field to the gauge field A 0 in the axial gauge. In both gauges, all degrees of freedom are physical making these gauge choices ideal for finding the bound-state equations and for renormalizability. Although the gauge independence of the physical observables such as the meson mass spectra following Regge trajectories may be guaranteed due to the gauge symmetry of QCD, the realization and interpretation of the identical physical results may depend on the gauge choices. Here, we discuss such difference in the realization of the confinement phenomena ala linear potential in the two different gauges, Coulomb vs. Axial, and highlight the gauge independent physical results expected. We also comment on the utility of the interpolation which leads to an alternative quasi-PDF that can be implemented in the lattice QCD without suffering from the large momentum boost.

Duggin, Hunter↗
DOE OSTI2014

Canonical quantization theory of general singular QED system of Fermi field interaction with generally decomposed gauge potential

Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system. -- Highlights: •We decompose the general gauge potential into two orthogonal parts according to general field theory. •We identify a new approach for quantizing the general singular QED system. •The results obtained are superior to those for the Lorentz gauge condition. •The theory presented solves dilemmas such as the nucleon spin crisis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field

In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term H{sub m} and a field term H{sub f}, and show that both H{sub m} and H{sub f} have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2012

An Intelligent Strain Gauge with Debond Detection and Temperature Compensation

The harsh rocket propulsion test environment will expose any inadequacies associated with preexisting instrumentation technologies, and the criticality for collecting reliable test data justifies investigating any encountered data anomalies. Novel concepts for improved systems are often conceived during the high scrutiny investigations by individuals with an in-depth knowledge from maintaining critical test operations. The Intelligent Strain Gauge concept was conceived while performing these kinds of activities. However, the novel concepts are often unexplored even if it has the potential for advancing the current state of the art. Maturing these kinds of concepts is often considered to be a tangential development or a research project which are both normally abandoned within the propulsion-oriented environment. It is also difficult to justify these kinds of projects as a facility enhancement because facility developments are only accepted for mature and proven technologies. Fortunately, the CIF program has provided an avenue for bringing the Intelligent Strain Gauge to fruition. Two types of fully functional smart strain gauges capable of performing reliable and sensitive debond detection have been successfully produced. Ordinary gauges are designed to provide test article data and they lack the ability to supply information concerning the gauge itself. A gauge is considered to be a smart gauge when it provides supplementary data relating other relevant attributes for performing diagnostic function or producing enhanced data. The developed strain gauges provide supplementary signals by measuring strain and temperature through embedded Karma and nickel chromium (NiCr) alloy elements. Intelligently interpreting the supplementary data into valuable information can be performed manually, however, integrating this functionality into an automatic system is considered to be an intelligent gauge. This was achieved while maintaining a very low mass. The low mass enables debond detection and temperature compensation to be performed when the gauge is utilized on small test articles. It was also found that the element's mass must be relatively small to avoid overbearing the desired thermal dissipation characteristics. Detecting the degradation of a gauge s bond was reliably achieved by correlating thermal dissipation with the bond s integrity. This was accomplished by precisely coupling a NiCr element with a Karma element for accurately interjecting and quantifying thermal energy. A finite amount of thermal energy is consistently placed in the gauge by electrically powering the NiCr element. The energy will only be temporarily stored before it begins to dissipate into the surrounding structure through the gauge bond. The ability to transmit the energy into the structure becomes greatly inhibited by any discontinuity in the bond s substrate. Therefore, the way the thermal dissipation occurs will reveal even the slightest change in the integrity of the bond.

Jensen, Scott L.↗
DOE OSTI2025

Fully gauge-fixed SU(2) Hamiltonian for quantum simulations

Here, we demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.

Lattice gauge theory↗
DOE OSTI2010

Comparison between length and velocity gauges in quantum simulations of high-order harmonic generation

We solve the time-dependent Schroedinger equation for atomic hydrogen in an intense field using spherical coordinates with a radial grid and a spherical harmonic basis for the angular part. We present the high-order harmonic spectra based on three different forms, the dipole, dipole velocity, and acceleration forms, and two gauges, the length and velocity gauges. The relationships among the harmonic phases obtained from the Fourier transform of the three forms are discussed in detail. Although quantum mechanics is gauge invariant and the length and velocity gauges should give identical results, the two gauges present different computation efficiencies, which reflects the different behavior in terms of characteristics of the physical couplings acting in the two gauges. In order to obtain convergence, more angular momentum states are required in the length gauge, while more grid points are required in the velocity gauge. At lower laser intensity, the calculation in the length gauge is faster than that in the velocity gauge, while at high laser intensity, the calculation in the velocity gauge is more efficient. The velocity gauge is also expected to be more efficient in higher-dimensional calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2004

Strain-Gauge Measurement of Weight of Fluid in a Tank

A method of determining the amount of fluid in a tank is based on measurement of strains induced in tank supports by the weight of the fluid. Unlike most prior methods, this method is nonintrusive: there is no need to insert instrumentation in the tank and, hence, no need to run wires, cables, or tubes through the tank wall. Also unlike most prior methods, this method is applicable even if the fluid in the tank is at supercritical pressure and temperature, because it does not depend on the presence of a liquid/gas interface (as in liquid-level-measuring methods). The strain gauges used in this method may be of two types: foil and fiber-optic. Four foil gauges (full bridge) are mounted on each of the tank-supporting legs. As the tank is filled or emptied, the deformation in each leg increases or decreases, respectively. Measured deformations of all legs are added to obtain a composite deformation indicative of the change in weight of the tank plus fluid. An initial calibration is performed by recording data at two points (usually, empty and full) for which the mass or weight of fluid is known. It is assumed that the deformations are elastic, so that the line passing through the two points can be used as a calibration curve of mass (or weight) of fluid versus deformation. One or more fiber-optic gauges may be used instead of the foil gauges. The resolution of the fiber-optic and foil gauges is approximately the same, but the fiber-optic gauges are immune to EMI (electromagnetic interference), are linear with respect to temperature over their entire dynamic range (as defined by the behavior of the sample), and measure thermally induced deformations as predictable signals. Conversely, long term testing has demonstrated that the foil gauges exhibit an erratic behavior whenever subjected to direct sun radiation (even if protected with a rubberized cover). Henceforth, for deployment in outdoor conditions, fiber-optic gauges are the only option if one is to rely on the system for an extended period of time when a recalibration procedure may not be acceptable. A set of foil gauges had been tested on the supports of a 500-gallon (1,900-liter) tank. The gauges were found to be capable of measuring the deformations (up to 22 micro-strain) that occurred during filling and emptying of the tank. The fluid masses calculated from the gauge readings were found to be accurate within 4.5 percent. However, the reliability of the foil gauges over a few hours was not acceptable. Therefore, the foil sensor system is acceptable for use only in controlled environments (complete shade, or indoors).

Figueroa, Jorge↗
DOE OSTI2023

Automated gauge reading and related systems, methods, and devices

Computing devices and methods for reading gauges are disclosed. A gauge reading method includes capturing image data corresponding to a captured image of one or more gauges, detecting one or more gauges in the captured image, cropping a detected gauge in the captured image to provide a use image including the detected gauge, and classifying the detected gauge to correlate the detected gauge with a template image. The gauge reading method also includes attempting to perform feature detection rectification on the use image to produce a rectified image of the detected gauge, performing template matching rectification on the use image to produce the rectified image responsive to a failure to perform the feature detection rectification, and estimating a gauge reading responsive to the rectified image. A computing device may implement at least a portion of a gauge reading method.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2011

Gauge invariant approach to low-spin anomalous conformal currents and shadow fields

Conformal low-spin anomalous currents and shadow fields in flat space-time of dimensions greater than or equal to four are studied. The gauge invariant formulation for such currents and shadow fields is developed. Gauge symmetries are realized by involving Stueckelberg and auxiliary fields. The gauge invariant differential constraints for anomalous currents and shadow fields and the realization of global conformal symmetries are obtained. Gauge invariant two-point vertices for anomalous shadow fields are also obtained. In the Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of conformal field theory. Light-cone gauge two-point vertices of the anomalous shadow fields are derived. The AdS/CFT correspondence for anomalous currents and shadow fields and the respective normalizable and non-normalizable solutions of massive low-spin anti-de Sitter fields is studied. The bulk fields are considered in a modified de Donder gauge that leads to decoupled equations of motion. We demonstrate that leftover on-shell gauge symmetries of bulk massive fields correspond to gauge symmetries of boundary anomalous currents and shadow fields, while the modified (Lorentz) de Donder gauge conditions for bulk massive fields correspond to differential constraints for boundary anomalous currents and shadow fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Quantum simulation of QED in Coulomb gauge

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. In this work, we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green’s function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of 10 8 for modest lattice size and accuracy level compared with the previous work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2007

Fiber-Optic Strain Gauge With High Resolution And Update Rate

An improved fiber-optic strain gauge is capable of measuring strains in the approximate range of 0 to 50 microstrains with a resolution of 0.1 microstrain. (To some extent, the resolution of the strain gauge can be tailored and may be extensible to 0.01 microstrain.) The total cost of the hardware components of this strain gauge is less than $100 at 2006 prices. In comparison with prior strain gauges capable of measurement of such low strains, this strain gauge is more accurate, more economical, and more robust, and it operates at a higher update rate. Strain gauges like this one are useful mainly for measuring small strains (including those associated with vibrations) in such structures as rocket test stands, buildings, oilrigs, bridges, and dams. The technology was inspired by the need to measure very small strains on structures supporting liquid oxygen tanks, as a way to measure accurately mass of liquid oxygen during rocket engine testing. This improved fiber-optic strain gauge was developed to overcome some of the deficiencies of both traditional foil strain gauges and prior fiber-optic strain gauges. Traditional foil strain gages do not have adequate signal-to-noise ratios at such small strains. Fiber-optic strain gauges have been shown to be potentially useful for measuring such small strains, but heretofore, the use of fiberoptic strain gauges has been inhibited, variously, by complexity, cost, or low update rate.

Figueroa, Fernando↗