Coulomb Gauge Research Articles

Coulomb confinement in the Hamiltonian limit

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, σC, to be about 3 times larger than the Wilson loop string tension, σF. It is far above the Zwanziger variational bound, σC≥σF. We argue that the value often reported in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension’s enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as σC/σF=2.0±0.4 and discuss its phenomenological implications. Published by the American Physical Society 2024

Influence of dynamical screening of four-quarks interaction on the chiral phase diagram

We investigate the effect of screening of the four-quarks contact interactions by the ring diagram at finite temperature and density in an effective chiral model inspired by QCD in the Coulomb gauge. As a consequence, a medium-dependent coupling naturally emerges which, in a class of chiral models, brings the chiral crossover temperature down to the value calculated in lattice QCD at low net-baryon density. Furthermore, it implies a stronger divergence of the chiral susceptibility at the critical point compared to the mean-field dynamics. At high densities, the screening induces a substantial instability region and its size depends on the regularization schemes. We discuss the properties of an effective potential for a class of models described by momentum-independent gap equations. In particular, we introduce the method to construct an approximate effective potential from the gap equations to determine the location of the first-order phase transition. Published by the American Physical Society 2024

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb gauge

Abstract Recently, it has been proposed to compute parton distributions from boosted correlators fixed in the Coulomb gauge within the framework of Large-Momentum Effective Theory. This method does not involve Wilson lines and could greatly improve the efficiency and precision of lattice QCD calculations. However, there are concerns about whether the systematic uncertainties from Gribov copies, which correspond to the ambiguity in lattice gauge-fixing, are under control. This work gives an assessment of the Gribov copies’ effect in the Coulomb-gauge-fixed quark correlators. We utilize different strategies for the Coulomb-gauge fixing, selecting two different groups of Gribov copies based on the lattice gauge configurations. We test the difference in the resulted spatial quark correlators in the vacuum and a pion state. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise. This demonstrates that the effect of the Gribov copies can be neglected in the practical lattice calculation of the quark parton distributions.

On some energy‐based variational principles in non‐dissipative magneto‐mechanics using a vector potential approach

AbstractThis contribution covers the variational‐based modeling of non‐dissipative magneto‐mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence‐free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re‐entrant corners.

Impact of gauge fixing precision on the continuum limit of nonlocal quark-bilinear lattice operators

We analyze the gauge fixing precision dependence of some nonlocal quark-bilinear lattice operators interesting in computing parton physics for several measurements, using five lattice spacings ranging from 0.032 to 0.121 fm. Our results show that gauge-dependent nonlocal measurements are significantly more sensitive to the precision of gauge fixing than anticipated. The impact of imprecise gauge fixing is significant for fine lattices and long distances. For instance, even with the typically defined precision of Landau gauge fixing of 10−8, the deviation caused by imprecise gauge fixing can reach 12%, when calculating the trace of Wilson lines at 1.2 fm with a lattice spacing of approximately 0.03 fm. Similar behavior has been observed in ξ gauge and Coulomb gauge as well. For both quasi-parton-distribution functions (quasi-PDFs) and quasi-transverse-momentum-dependent PDFs operators renormalized using the regularization independent momentum subtraction (RI/MOM) scheme, convergence for different lattice spacings at long distance is only observed when the precision of Landau gauge fixing is sufficiently high. To describe these findings quantitatively, we propose an empirical formula to estimate the required precision. Published by the American Physical Society 2024

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

Atomic Data for Astrophysically Important Spectral Lines of Singly Ionized Nitrogen

Nitrogen lines are widely observed in astrophysical spectra and provide important diagnostics for plasma properties. In this work, we present extended calculations for accurate energy levels, electric dipole radiative transition parameters, and lifetimes for the lowest 102 states of the 2s 22p 2, 2s2p 3, 2s2p 23s, 2s 22p{n 1 l, n 2 d, 4f}(n 1 = 3–5, l = s, p, n 2 = 3, 4), and 2p 4 configurations of N ii within the framework of the fully relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. These data are useful for modeling astrophysical spectra, for example, for nitrogen abundance determinations in early B-type stars, and for studying the compositions and plasma properties of H ii regions and planetary nebulae. Our computed transition parameters are compared with available experimental and theoretical data. The accuracy of the calculations is also assessed via a statistical analysis of the differences between the transition rates in the Babushkin and Coulomb gauges and by consideration of cancellation factors. In this way, 201 of the 1656 transitions computed in this work are estimated to be from accurate to better than 3%, corresponding to an accuracy class of A.

Photon propagator for inflation in the general covariant gauge

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell’s fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.

A structure-preserving algorithm for Vlasov–Darwin system conserving charge, canonical momentum, and Hamiltonian

In this paper, a conservative numerical method for the Vlasov–Darwin system is proposed. The Darwin model was assumed to be valid only in the Coulomb gauge, but recently this model has also been extended to the Lorenz gauge [1]. The Darwin model, based on the Lorenz gauge, exhibits a good symmetry between scalar and vector potentials, making the proofs of physical constraints relatively easy. In addition, the total energy was believed to be one of the conservative quantities of the Vlasov–Darwin system. However, the improved theory suggests that the Hamiltonian is the conservative quantity rather than the total energy. The structure-preserving scheme proposed in this paper exactly maintains the Lorenz gauge and the conservation laws of charge, canonical momentum, and Hamiltonian in discrete form.

Parton distributions from boosted fields in the Coulomb gauge

We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice. Published by the American Physical Society 2024

Constituent model of light hybrid meson decays

A model of light hybrid mesons and their strong decays is developed. The model employs a gluonic quasiparticle to describe low energy gluodynamics and uses the QCD Hamiltonian in Coulomb gauge to guide the construction of states and decay amplitudes. We compute the partial widths of the twelve low lying isovector and vector hybrids. Implications of these results on hybrid searches are also made, with the chief conclusions being that direct observation of the vector states will be difficult, that a hybrid π(1800) has distinctive decay characteristics, a narrow η(1900) hybrid should exist, an η1(1750) should be sought, and that the exotic nature of JPC=2−+ hybrid mesons should be discernible with sufficient data. We argue that the isovector π2 hybrid has been discovered, giving a total of four possible hybrid mesons, π1(1600), η1(1855), π(1800), and π2(2360), which appear to be filling out the low lying hybrid supermultiplet in the expected fashion. Published by the American Physical Society 2024

Remnants of quark model in lattice QCD simulation in the Coulomb gauge

Remnants of quark model in lattice QCD simulation in the Coulomb gauge

Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities.

It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

Potentials and fields of a charge set suddenly from rest into uniform motion

The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly into uniform motion. The modified potentials are shown to satisfy the requisite inhomogeneous wave equations. The gauge function of the transformation of these potentials to the Coulomb gauge is calculated in closed form. It is validated by confirming that the Coulomb-gauge vector potential that is calculated using it yields together with the Coulomb-gauge scalar potential the same electric and magnetic fields as those calculated with the Lorenz-gauge potentials.

Topology of weak $G$-bundles via Coulomb gauges in critical dimensions

Topology of weak $G$-bundles via Coulomb gauges in critical dimensions

The Coulomb Gauge in Non-associative Gauge Theory

The Coulomb Gauge in Non-associative Gauge Theory

Two-dimensional Axisymmetric Modeling of the Magnetic Field for High-voltage Gas Circuit Breakers

High fidelity numerical analyses of high-voltage gas circuit breakers have been conducted at Hitachi Energy Research with an in-house CFD-based arc simulation tool. The tool extends the capability of a commercial flow solver (ANSYS Fluent) to represent physical phenomena at play in a high voltage circuit breaker during a breaking operation, such as magnetostatics, polymeric and metal evaporation, and arc-network interaction. This work describes the implementation of the Biot-Savart law for computing the magnetic field generated by an electric arc under the magnetostatic approximation and in two--dimensional axisymmetric conditions. The implementation is compared to the reference one based on the magnetic vector potential formulation of the Amp`ere’s law in the Coulomb gauge. The limitations of the two formulations are discussed and their numerical accuracy compared.

Local well-posedness of the Einstein-Yang-Mills system in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge

We study the local well-posedness of the Einstein-Yang-Mills equations in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge. In this choice of gauge, the complete Einstein-Yang-Mills equations reduce to a coupled elliptic-hyperbolic system. We establish the existence of a unique, local, continuous-in-time solution to this coupled system. This yields an “in time” continuation criteria of the solutions which are to be used in the potential future proof of improved continuation criteria for this coupled system utilizing Moncrief’s light cone estimate technique.

On the global well-posedness of the Einstein–Yang–Mills system

In this paper, we present a partial result on the global well-posedness of the Cauchy problem for the Einstein–Yang–Mills system in constant mean extrinsic curvature spatial harmonic and generalized Coulomb gauges as introduced in the work of Mondal [arXiv:2112.14273 (2021)]. We give a small-data global existence theorem for a family of n + 1 dimensional spacetimes with n ≥ 4, utilizing energy arguments presented in the work of Andersson and Moncrief [J. Differ. Geom. 89, 1–47 (2009)]. We observe that these energy arguments will fail for n = 3 due to the conformal invariance of 3 + 1 Yang–Mills equations and present a gauge-covariant formulation of the Einstein–Yang–Mills system in 3 + 1 dimensions to show that an energy argument cannot be used to prove the global well-posedness result, regardless of the choice of gauge.

Extended atomic data for oxygen abundance analyses

As the most abundant element in the universe after hydrogen and helium, oxygen plays a key role in planetary, stellar, and galactic astrophysics. Its abundance is especially influential in terms of stellar structure and evolution, and as the dominant opacity contributor at the base of the Sun’s convection zone, it is central to the discussion on the solar modelling problem. However, abundance analyses require complete and reliable sets of atomic data. We present extensive atomic data for O I by using the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. We provide the lifetimes and transition probabilities for radiative electric dipole transitions and we compare them with results from previous calculations and available measurements. The accuracy of the computed transition rates is evaluated by the differences between the transition rates in Babushkin and Coulomb gauges, as well as via a cancellation factor analysis. Out of the 989 computed transitions in this work, 205 are assigned to the accuracy classes AA-B, that is, with uncertainties smaller than 10%, following the criteria defined by the Atomic Spectra Database from the National Institute of Standards and Technology. We discuss the influence of the new log(gf) values on the solar oxygen abundance, ultimately advocating for log єO = 8.70 ± 0.04.