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Register a new userTurbulence in nonabelian gauge theory
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Kolmogorov wave turbulence plays an important role for the thermalization process following plasma instabilities in nonabelian gauge theories. We show that classical-statistical simulations in SU(2) gauge theory indicate a Kolmogorov scaling exponent known from scalar models. In the range of validity of resummed perturbation theory this result is shown to agree with analytical estimates. We study the effect of classical-statistical versus quantum corrections and demonstrate that the latter lead to the absence of turbulence in the far ultraviolet.
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In the present paper we study the limit of zero mass in nonabelian gauge theories both with Higgs mechanism and in the nonlinear realization of the gauge group (Stueckelberg mass). We argue that in the first case the longitudinal modes undergo a metamorphosis process to the Goldstone scalar modes, while in the second we guess a decoupling process associated to a phase transformation. The two scenarios yield strikingly different behaviors at high energy, mainly ascribed to the presence of a massless Higgs doublet among the physical modes in the case of Higgs mechanism (i.e. not only the Higgs boson). The aim of this work is to show that the problem of unitarity at high energy in nonabelian gauge theory with no Higgs boson can open new perspectives in quantum field theory.
We compute nonequilibrium dynamics of plasma instabilities in classical-statistical lattice gauge theory in 3+1 dimensions. The simulations are done for the first time for the SU(3) gauge group relevant for quantum chromodynamics. We find a qualitatively similar behavior as compared to earlier investigations in SU(2) gauge theory. The characteristic growth rates are about 25 % lower for given energy density, such that the isotropization process is slower. Measured in units of the characteristic screening mass, the primary growth rate is independent of the number of colors.
We compute nonequilibrium dynamics for classical-statistical SU(2) pure gauge theory on a lattice. We consider anisotropic initial conditions with high occupation numbers in the transverse plane on a characteristic scale ~ Q_s. This is used to investigate the very early stages of the thermalization process in the context of heavy-ion collisions. We find Weibel or primary instabilities with growth rates similar to those obtained from previous treatments employing anisotropic distributions of hard modes (particles) in the weak coupling limit. We observe secondary growth rates for higher-momentum modes reaching substantially larger values and we analyse them in terms of resummed loop diagrams beyond the hard-loop approximation. We find that a coarse grained pressure isotropizes bottom-up with a characteristic inverse rate of gamma^{-1} ~ 1 - 2 fm/c for coarse graining momentum scales of p < 1 GeV choosing an initial energy density for RHIC of epsilon = 30 GeV/fm^3. The nonequilibrium spatial Wilson loop is found to exhibit an area law and to become isotropic on a similar time scale.
We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition.
We determine the time evolution of fluctuations of the Polyakov loop after a quench into the deconfined phase of SU(3) gauge theory from a simple classical relativistic Lagrangian. We compare the structure factors, which indicate spinodal decomposition followed by relaxation, to those obtained via Markov Chain Monte Carlo techniques in SU(3) lattice gauge theory. We find that the time when the structure factor peaks diverges like $sim 1/k^2$ in the long-wavelength limit. This is due to formation of competing Z(3) domains for configurations where the Polyakov loop exhibits non-perturbatively large variations in space, which delay thermalization of long wavelength modes. For realistic temperatures, and away from the extreme weak-coupling limit, we find that even modes with $k$ on the order of $T$ experience delayed thermalization. Relaxation times of very long wavelength modes are found to be on the order of the size of the system; thus, the dynamics of competing domains should accompany the hydrodynamic description of the deconfined vacuum.
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