Induced Color Current by Gluon in Background QCD

In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.

Physical Review D, 2006

We study the non-perturbative production of gluon pairs from a constant SU(3) chromo-electric background field via the Schwinger mechanism. We fix the covariant background gauge with an arbitrary gauge parameter α. We determine the transverse momentum distribution of the gluons, as well as the total probability of creating pairs per unit space time volume. We find that the result is independent of the covariant gauge parameter α used to define arbitrary covariant background gauges. We find that our non-perturbative result is both gauge invariant and gauge parameter α independent.

Physical Review D, 1973

The considerations of,the first paper in this series are extended to non-Abelian gauge models of the strong, weak, and electromagnetic interactions. It is shown that for a large class of such theories, the strong interactions naturally conserve parity and strangeness, and possibly isospin and other quantum numbers as well. The corrections of second order in gauge couplings to such natural symmetries are convergent. In addition to the ordinary photon-exchange term, these corrections include other terms of order e, which take the form of shifts in the effective quark mass matrix, and which automatically conserve parity and strangeness. In theories with free-field asymptotic behavior, these order-n mass shifts may be correctly calculated ignoring all effects of the strong interactions. It is suggested that in such theories, the strong gauge group is not broken, and that the infrared divergences associated with the massless vector gluons prevent the production of quarks or gluons in collisions of ordinary hadrons.

Theoretical and Mathematical Physics, 2006

We investigate the question about the transversality of the gluon polarization tensor in a homogeneous chromomagnetic background field. We re-derive the non transversality known from a pure one loop calculation using the Slavnov-Taylor identities. In addition we generalize the procedure to arbitrary gauge fixing parameter ξ and calculate the ξ-dependent part of the polarization tensor.

Journal of Physics A: Mathematical and Theoretical, 2008

In SU(2) gluodynamics, the structure of the exact Green function of neural gluons in an Abelian homogeneous magnetic field at finite temperature is derived. It is expressed through 10 tensors and corresponding form factors. These tensors constitute an algebra with respect to anticommutation. The structure constants of the algebra are calculated. The spectrum of gluons is derived from the pole positions of this Green function for the case of form factors computed in one-loop order. The high temperature asymptotics for the form factors, the Debye mass, the magnetic mass and the spectra of different gluon states in this limit are calculated.

Physical Review D, 2000

The flow-equation method of continuous unitary transformations is used to eliminate the minimal quark-gluon interaction in the light-front quantized QCD Hamiltonian. The coupled differential equations in the two lowest Fock sectors correspond to the renormalization of the light-front gluon mass and the generation of an effective quark-antiquark (as well as gluon-gluon) interaction. The original gauge field coupling is completely eliminated, even in the presence of degenerate states connected by this interaction. Further, a more singular 1/q 4 behavior for the quark and gluon effective interactions at small gluon momenta is obtained, due to the asymptotic behavior of the effective gluon mass for small cutoff. We discuss the consequences of this asymptotic behavior and possible confinement implications.

Physical Review D, 2003

We solve the collisionless transport equations of a quark-gluon plasma interacting through mean chromodynamic fields. The system is assumed to be translation invariant in one or more space-time directions. We present exact solutions that hold if the vector gauge fields in the direction of the translation invariance commute with their covariant derivatives. We also solve the equations perturbatively when the commutation condition is relaxed. Further, we derive the color current and the associated effective action. For the static quasi-equilibrium system, our results reproduce the full one-loop effective action of QCD in the presence of constant background fields, where the above mentioned commutation condition is satisfied.

Australian Journal of Physics, 1997

Physical Review D, 2008

We calculate the polarization tensor of charged gluons in a Abelian homogeneous magnetic background field at finite temperature in one loop order Lorentz background field gauge in full generality. Thereby we first determine the ten independent tensor structures. For the calculation of the corresponding form factors we use the Schwinger representation and represent form factors as double parametric integrals and a sum resulting from the Matsubara formalism used. The integrands are given explicitly in terms of hyperbolic trigonometric functions. Like in the case of neutral gluons, the polarization tensor is not transversal. Out of the tensor structures, seven are transversal and three are not. The nontransversal part follows explicitly from our calculations.

International Journal of Modern Physics A, 2005

The color–flavor transformation is applied to the U (Nc) lattice gauge model, in which the gauge theory is induced by a heavy chiral scalar field sitting on lattice sites. The flavor degrees of freedom can encompass several "generations" of the auxiliary field, and for each generation, remaining indices are associated with the elementary plaquettes touching the lattice site. The effective, color–flavor transformed theory is expressed in terms of gauge singlet matrix fields carried by lattice links. The effective action is analyzed for a hypercubic lattice in arbitrary dimension. The saddle points equations of the model in the large-Nc limit are discussed.