Quark confinement physics from quantum chromodynamics

We show the construction of the dual superconducting theory for the confinement mechanism from QCD in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. We find that essence of infrared abelian dominance is naturally understood with the off-diagonal gluon mass m_off ≈- 1.2GeV induced by the MA gauge fixing. In the MA gauge, the off-diagonal gluon amplitude is forced to be small, and the off-diagonal gluon phase tends to be random. As the mathematical origin of abelian dominance for confinement, we demonstrate that the strong randomness of the off-diagonal gluon phase leads to abelian dominance for the string tension. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system. We investigate the monopole-current system in the MA gauge by analyzing the dual gluon field B_μ. We evaluate the dual gluon mas as m_B = 0.4 0.5GeV in the infrared region, which is the lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Owing to infrared abelian dominance and infrared monopole condensation, QCD in the MA gauge is describable with the dual Ginzburg-Landau theory.     

Convergence of Feynman integrals in Coulomb gauge QCD

At 2-loop order, Feynman integrals in the Coulomb gauge are divergent over the internal energy variables. Nevertheless, it is known how to calculate the effective action, provided that the external gluon fields are all transverse. We show that, for the two-gluon Greens function as an example, the method can be extended to include longitudinal external fields. The longitudinal Greens functions appear in the BRST identities. As an intermediate step, we use a flow gauge, which interpolates between the Feynman and Coulomb gauges.     

On the stability of the chiral vacuum

Zeitschrift für Physik C Particles and Fields - The stability of the chiral vacuum is explored in Coulomb gauge QCD, in the Breit frame. We find that perturbative Coulomb and transverse gluon...     

Gluon Propagator and Heavy Quark Potential in an Anisotropic QCD Plasma

The hard-loop resummed propagator in an anisotropic QCD plasma in general linear gauges are computed. We get the explicit expressions of the gluon propagator in covariant gauge, Coulomb gauge and temporal axial gauge. Considering one gluon exchange, the potential between heavy quarks is defined through the Fourier transform of the static propagator. We find that the potential exhibits angular dependence and that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment.     

Linear response of the hot QCD plasma from the gluon propagator

Linear response theory is used to express the positions of the physical poles in the finite temperature gluon propagator in terms of the components of the proper self-energy. The analysis is valid in a wide class of covariant and non-covariant gauges, for both transverse and non-transverse self-energies. The formalism is then applied to the calculation at the one loop level of the bare plasma parameters and of Landau ghosts in two classes of gauges: the covariant gauge and a one parameter family of non-covariant gauges which interpolate between the static temporal gauge and the Coulomb gauge.     

Canonical quantization and chromodynamics in a spherical cavity

The canonical quantization formalism is applied to the Lagrange density of chromodynamics, which includes gauge fixing and Faddeev-Popov ghost terms in a general covariant gauge. We develop the quantum theory of the interacting fields in the Dirac picture, based on the Gell-Mann and Low theorem and the Dyson expansion of the time evolution operator. The physical states are characterized by their invariance under Becchi-Rouet-Stora transformations. Subsequently, confinement is introduced phenomenologically by imposing, on the quark, gluon, and ghost field operators, the linear boundary conditions of the MIT bag model at the surface of a spherically symmetric and static cavity. Based on this formalism, we calculate, in the Feynman gauge, all nondivergent Feynman diagrams of second order in the strong coupling constantg. Explicit values of the matrix elements are given for low-lying quark and gluon cavity modes.     

The effective potential of the confinement order parameter in the Hamiltonian approach

The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. Neglecting the ghost and using the perturbative gluon energy one recovers the Weiss potential. From the full non-perturbative potential calculated within a variational approach a critical temperature of the deconfinement phase transition of 269 MeV is found for the gauge group SU(2).     

A nonperturbative variational approach to the vacuum structure in quantum chromodynamics

We study the vacuum structure in QCD in a nonperturbative manner using a variational approach with gluon condensates. We show that in Coulomb gauge as the coupling becomes moderately strong, the perturbative vacuum of QCD becomes unstable leading to gluon condensates and a gauge dependent effective mass for the gluons related to the gauge independent value of 〈vac‖G _μν ^a G ^aμν‖vac〉 of Shifmanet al.     

Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.     

Asymptotic behaviour of classical Yang-Mills fields in Minkowski space

We show how to define incoming and outgoing asymptotic fields for classical solutions of the Yang-Mills field equations without fixing the gauge. It is then seen that the Gribov ambiguities for putting the field in the Coulomb gauge reduce asymptotically to a field-independent, infinite parameter group of gauge transformations. This obscures the notion of color charge already at the classical level.     

Hidden spurious sources in axial gauge propagators

We show that charge carrying propagators in axial gauges involve spurious sources that move along the rays of gauge fixing. Although these spurious sources are hidden in the axial gauge in question, they are manifest when the same propagator is viewed in other gauges. Therefore, they influence the propagation of the dynamical fields. Thus the naive electron propagator in axial gauge quantum electrodynamics does not have the spectrum of a free, mass-renormalized electron. We confine our remarks to quantum electrodynamics here. In the sequel the implication for axial gauge quark and gluon propagators in quantum chromodynamics is discussed. Gauge-independent propagators do not suffer this affliction.     

The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge

The Dyson-Schwinger equation for the ghost-gluon vertex of the Hamiltonian approach to Yang-Mills theory in Coulomb gauge is solved at one-loop level using as input the non-perturbative ghost and gluon propagators previously determined within the variational approach. The obtained ghost-gluon vertex is IR finite but IR enhanced compared to the bare one by 15%-25%, depending on the kinematical momentum regime.     

QCD plasma parameters in axial gauge

Within the framework of imaginary time formalism we investigate the structure of the gluon polarization tensor and relate its structure functions to the dispersion relation of plasma eigenmodes. To one loop order, we calculate the transversal structure function to leading order in the high temperature expansion as well as the first subleading order contribution in the long wavelength limit. The result is used to express the dynamical mass and the damping constant for transversal plasma eigenmodes. The aim of our present paper is a systematic discussion of the gauge fixing vector dependence of the damping constant. In the limit of temporal axial gauge we encounter a negative damping constant contradicting previous results.     

Dual Meissner effect and magnetic displacement currents

The dual Meissner effect is observed without monopoles in quenched SU(2) QCD with Landau gauge fixing. Magnetic displacement currents that are time-dependent Abelian magnetic fields act as solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary for the dual Meissner effect. A mean-field calculation suggests that the dual Meissner effect through the mass generation of the Abelian electric field is related to a gluon condensate A(a)(mu)A(a)(mu) not equal 0 of mass dimension 2.     

A quasi-temporal gauge

We prove that a complete fixing of the temporal gauge,A _o =0, in which one imposesa subsidiary gauge condition, such as, for instance ?_i A _i (x,t ₀) = 0 leads to consistent formulation of the theory with simple Feynman rulesand a well defined gluon propagator. The correct exponentiation of the time dependence of the Wilson loop has been checked to occur up to order g⁴.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

Quadrupole moments of hadrons

We study an Abelian Higgs model in three, four and five dimensions using the mean field perturbation expansion with covariant gauge fixing. In four and five dimensions the mean field analysis shows three phases; a confined phase, a Coulomb phase with massless spin waves, and a Higgs phase in which the spin waves aquire a mass. The Higgs and confined phases are shown to be connected. In three dimensions we find a single phase.