Temporal Axial Gauge Research Articles

Entropy Production in Gluodynamics in Temporal Axial Gauge in 2+1 Dimensions

Entropy production in non-Abelian gauge theory is discussed in the limit of vanishing classical fields. Based on the Kadanoff-Baym equation with the leading order self-energy in the temporal axial gauge, the kinetic entropy is introduced and is proven to increase for a given self-energy. Numerical simulation of the Kadanoff-Baym equation for the non-Abelian gauge theory is performed in 2+1 dimensions. Starting from anisotropic distribution in momentum space, relaxation to isotropic distribution proceeds and the entropy is produced due to off-shell scattering of massive transverse polarization mode as expected from the proof of the H-theorem.

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.

Collective modes of ultra-relativistic magnetoactive electron plasma

Collective modes of ultra-relativistic electron plasma embedded in an ambient weak magnetic field are derived. Employing Maxwell equations in the four-dimensional Minkowski space and using the Vlasov model, polarization tensor is calculated and dispersion relations are obtained for both parallel and perpendicular propagations in the temporal axial gauge. Some interesting limiting cases are also discussed.

QCD pressure and the trace anomaly

Exact relations between the QCD thermal pressure and the trace anomaly are derived. These are used, first, to prove the equivalence of the thermodynamic and the hydrodynamic pressure in equilibrium in the presence of the trace anomaly, closing a gap in previous arguments. Second, in the temporal axial gauge a formula is derived which expresses the thermal pressure in terms of a Dyson-resummed two-point function. This overcomes the infrared problems encountered in the conventional perturbation-theory approach.

Gluon self-energy in the Coulomb and temporal axial gauges via the pinch technique.

The $S$-matrix pinch technique is used to derive an effective gluon self-energy to one-loop order, when the theory is quantized in the Coulomb gauge (CG) and in the temporal axial gauge (TAG). When the pinch contributions are added, the gluon self-energies calculated in CG and TAG turn out to be identical and coincide with the result previously obtained with covariant gauges. The issue of gauge independence of several quantities in hot QCD is discussed from the pinch technique point of view. It is also pointed out that the spurious singularities which appear in TAG calculations cancel out once the pinch contributions are combined.

Difficulties in formulating an imaginary-time formalism of temporal axial gauge at finite T

Following the successful construction of the finite T real-time formalism in temporal axial gauge, we attempt to further study the equivalent new imaginary-time formalism of James and Landshoff based on the same Hamiltonian approach in the hope that it will provide the answer to Debye screening in QCD. It turns out that, unlike in the real-time case, energy conservation does not hold because of the unusual representation of the longitudinal field forced upon by the Hamiltonian formulation.

Gauge-independent thermal β function in Yang-Mills theory

It is proposed to use the pinch technique (PT) to obtain the gauge-independent thermal β function in a hot Yang-Mills gas. Calculations of the thermal β function are performed at one-loop level in four different gauges, (i) the background field method with an arbitrary gauge, (ii) the Feynman gauge, (iii) the Coulomb gauge, and (iv) the temporal axial gauge, and they yield the same result in all four cases.

Difficulties in formulating an imaginary-time formalism of temporal axial gauge at finite T

Following the successful construction of the finite T real-time formalism in temporal axial gauge, we attempt to further study the equivalent new imaginary-time formalism of James and Landshoff based on the same Hamiltonian approach in the hope that it will provide the answer to Debye screening in QCD. It turns out that, unlike in the real-time case, energy conservation does not hold because of the unusual representation of the longitudinal field forced upon by the Hamiltonian formulation.

Finite temperature formalism for non-Abelian gauge theories in the physical phase space.

We establish a new framework of finite temperature field theory for Yang-Mills theories in the physical phase space eliminating all unphysical degrees of freedom. Relating our method to the imaginary time formalism of James and Landshoff in the temporal axial gauge, we calculate the two-loop pressure and provide a systematic and unique method to construct the additional vertices encountered in their approach.

Non-Debye screening in high temperature QCD?

We study the non-abelian, gauge invariant, screening potential between two charges in a quark-gluon plasma. Using Braaten and Pisarski resummed perturbation theory in temporal axial gauge, we find a repulsive power screened potential which behaves as ∼ 1 r 6 at large distance. This questions either the physical meaning of the Debye mass or the known pragmatic treatment of the temporal axial gauge propagator.

Nonabelian Debye screening in one-loop resummed perturbation theory

Debye screening of static chromoelectric fields at high temperature is investigated at next-to-leading order through one-loop resummed perturbation theory. At this order the gluon propagator appears to give rise to strong deviations from a Yukawa form of screening. Generally, an oscillatory behavior is found which asymptotically becomes repulsive, but in a gauge-dependent manner. However, these features are strongly sensitive to the existence of screening of static magnetic fields. It is shown that a small magnetic screening mass can restore exponential screening with a gauge-independent value of the screening mass, which depends logarithmically on the magnitude of the magnetic mass. Recent results obtained in temporal axial gauge, which instead indicate an asymptotic (repulsive) power-law behaviour of screening, are also critically discussed. In order to arrive at a gauge-invariant treatment of chromoelectric screening, Polyakov loop correlations are considered, both with and without dynamical gauge symmetry breaking. Again a crucial sensitivity to the scale of magnetic screening is found. A detailed comparison of the perturbative results with recent high-precision lattice simulations of the SU(2) Polyakov loop correlator is made, which are found to agree well with the perturbative result in the symmetric phase when a magnetic mass ∼ g 2 T/4 is included.

The nonabelian screening potential beyond the leading order

The nonabelian screening potential is calculated in the temporal axial gauge. The Slavnov-Taylor identity is used to construct the three-gluon vertex function from the inverse gluon propagator. After solving the Schwinger-Dyson equation beyond leading order we find that the obtained momentum dependence of the gluon self-energy at high temperature does not correspond to an attractive QCD-Debye potential, but instead it is repulsive and power behaved ( ⋍ 1/r 6 ) at large distance.

Gluon mass and gauge consistency constraints

The exact Dyson-Schwinger equation for the effective gluon mass in the temporal axial gauge is shown to reduce to evaluation of a single two-loop skeleton graph as a consequence of the Slavnov-Taylor-Ward-Takahashi conditions for gauge consistency. Not only does the exact one-loop contribution, comprising almost all previous work, and the entire longitudinal part vanish identically, as previously known, but also the number of independent functions to be self-consistently determined is reduced so that it is no longer necessary to consider the four-gluon vertex function, even at the full two-loop level.

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.

Pole prescription in axial gauge at finite temperature

>We establish Yang-Mills theory at finite temperature in axial gauge. We encounter the breakdown of the Hata-Kugo expression for the partition function in the special choice of temporal axial gauge. For n ≠ 0 the finite temperature propagator is calculated in both the imaginary time formalism and the real time formalism. In the latter we recover the Leibbrandt-Mandelstam prescription in the lijit T→0. As a check we calculate the mean energy to lowest order.

A test for the temporal axial gauge at finite temperature: The two-loop gluon-interaction pressure calculated in the real time formalism

Using the 2×2 matrix propagator previously found by the author, we calculate the interaction pressure of the gluon plasma to two loops at high temperature using the temporal axial gauge in the real time formalism. This quantity is gauge invariant and is thus a good check for the validity of the Feynman rules found for the temporal gauge at finite temperature. Our result is identical to that found by Landsman et al. and Kapusta using covariant gauges in the real and imaginary time formalisms respectively.

Lattice simulation of the anomalous gluon contribution to the proton spin.

The magnitude of the gluon contribution to the proton spin induced by the triangle anomaly diagram in the quark axial current is estimated by means of a lattice QCD simulation (in the temporal axial gauge) of the polarized-proton matrix element of the anomalous current 〈ps\ensuremath{\Vert}${\mathit{K}}_{\mathrm{\ensuremath{\mu}}}$\ensuremath{\Vert}ps〉. The result of the simulation is that the fractional contribution of the gluon anomaly to the proton spin, -(3\ensuremath{\alpha}/2\ensuremath{\pi})\ensuremath{\Delta}g, is less than 0.05 in magnitude. This is much too small to affect the basic interpretation of the E.M.C. experiment, namely that the quark spins are responsible for very little, if any, of the proton spin.

The temporal axial gauge at finite temperature explored using the real time formalism

The temporal axial gauge is discussed at zero temperature and extended to finite temperature. A set of Feynman rules is determined within the real-time formalism which allows one to do perturbation theory at finite temperature using the temporal gauge. As a demonstration of the Feynman rules derived we do a simple linear response analysis for the gluon plasma at high temperature. This analysis yields a positive damping constant to one loop order in the long-wavelength limit. The problem of the imaginary-time formalism is discussed.

Behaviour of gluons at high temperature

The screening of colour electric and magnetic fields and plasma oscillations in a high-temperature gluon plasma are investigated using linear response theory and self-consistent nonperturbative solutions to the Schwinger-Dyson equation. Static electric fields are screened, with m el 2 = 1 3 g 2NT 2 − ( 3 π )( 1 6 g 2N) 3 2 T 2 . This result is proven to be gauge invariant in two ways: by computing π 00 in temporal axial, Coulomb and covariant gauges, and by computing the physical free energy of a heavy quark pair in the plasma in temporal axial gauge. To order g 3 static magnetic fields are not screened.

Possible solution to the plasmon puzzle in hot SU( N) gluon matter

We present a calculation of the plasmon contribution to the thermodynamical potential for hot SU( N) gluon matter in the temporal axial gauge. This result together with a recent non-perturbative calculation of the colour-electric gluon mass in the same gauge leads to a modified plasmon contribution which is always smaller than the g 2-contribution, thus resolving the plasmon puzzle.