Optimization of perturbative similarity renormalization group for Hamiltonians with asymptotic freedom and bound states

A model Hamiltonian that exhibits asymptotic freedom and a bound state, is used to show on example that similarity renormalization group procedure can be tuned to improve convergence of perturbative derivation of effective Hamiltonians, through adjustment of the generator of the similarity transformation. The improvement is measured by comparing the eigenvalues of perturbatively calculated renormalized Hamiltonians that couple only a relatively small number of effective basis states, with the exact bound state energy in the model. The improved perturbative calculus leads to a few-percent accuracy in a systematic expansion.Comment: 6 pages of latex, 4 eps figure

Dispersion relations and speeds of sound in special sectors for the integrable chain with alternating spins

Based on our previous analysis \cite{doerfel3} of the anisotropic integrable chain consisting of spins $s=1/2$ and $s=1$ we compare the dispersion relations for the sectors with infinite Fermi zones. Further we calculate the speeds of sound for regions close to sector borders, where the Fermi radii either vanish or diverge, and compare the results.Comment: 11 pages, LaTeX2e, uses iopart.cls,graphicx.sty and psfrag.sty, 2 figure

Asymptotic Freedom and Bound States in Hamiltonian Dynamics

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.Comment: plain latex file, 15 pages, 6 latex figures 1 page each, 1 tabl

Whitening of the Quark-Gluon Plasma

Parton-parton collisions do not neutralize local color charges in the quark-gluon plasma as they only redistribute the charges among momentum modes. We discuss color diffusion and color conductivity as the processes responsible for the neutralization of the plasma. For this purpose, we first compute the conductivity and diffusion coefficients in the plasma that is significantly colorful. Then, the time evolution of the color density due to the conductivity and diffusion is studied. The conductivity is shown to be much more efficient than the diffusion in neutralizing the plasma at the scale longer than the screening length. Estimates of the characteristic time scales, which are based on close to global equilibrium computations, suggest that first the plasma becomes white and then the momentum degrees of freedom thermalize.Comment: 9 pages, revised, to appear in Phys. Rev.

Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization

Hamiltonian light-front field theory can be used to solve for hadron states in QCD. To this end, a method has been developed for systematic renormalization of Hamiltonian light-front field theories, with the hope of applying the method to QCD. It assumed massless particles, so its immediate application to QCD is limited to gluon states or states where quark masses can be neglected. This paper builds on the previous work by including particle masses non-perturbatively, which is necessary for a full treatment of QCD. We show that several subtle new issues are encountered when including masses non-perturbatively. The method with masses is algebraically and conceptually more difficult; however, we focus on how the methods differ. We demonstrate the method using massive phi^3 theory in 5+1 dimensions, which has important similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final published versio

Spin-2 Amplitudes in Black-Hole Evaporation

Quantum amplitudes for $s=2$ gravitational-wave perturbations of Einstein/scalar collapse to a black hole are treated by analogy with $s=1$ Maxwell perturbations. The spin-2 perturbations split into parts with odd and even parity. We use the Regge-Wheeler gauge; at a certain point we make a gauge transformation to an asymptotically-flat gauge, such that the metric perturbations have the expected falloff behaviour at large radii. By analogy with $s=1$, for $s=2$ natural 'coordinate' variables are given by the magnetic part $H_{ij} (i,j=1,2,3)$ of the Weyl tensor, which can be taken as boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the data on the initial surface $\Sigma_I$ to be exactly spherically-symmetric. The (large) Lorentzian proper-time interval between $\Sigma_I$ and $\Sigma_F$, measured at spatial infinity, is denoted by $T$. We follow Feynman's $+i\epsilon$ prescription and rotate $T$ into the complex: $T\to{\mid}T{\mid} \exp(-i\theta)$, for $0<\theta\leq\pi/2$. The corresponding complexified {\it classical} boundary-value problem is expected to be well-posed. The Lorentzian quantum amplitude is recovered by taking the limit as $\theta\to 0_+$. For boundary data well below the Planck scale, and for a locally supersymmetric theory, this involves only the semi-classical amplitude $\exp(iS^{(2)}_{\rm class}$, where $S^{(2)}_{\rm class}$ denotes the second-variation classical action. The relations between the $s=1$ and $s=2$ natural boundary data, involving supersymmetry, are investigated using 2-component spinor language in terms of the Maxwell field strength $\phi_{AB}=\phi_{(AB)}$ and the Weyl spinor $\Psi_{ABCD}=\Psi_{(ABCD)}$

Renormalized Effective QCD Hamiltonian: Gluonic Sector

Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.Comment: 25 pages, no figures, revte

Nonextensive hydrodynamics for relativistic heavy-ion collisions

The nonextensive one-dimensional version of a hydrodynamical model for multiparticle production processes is proposed and discussed. It is based on nonextensive statistics assumed in the form proposed by Tsallis and characterized by a nonextensivity parameter $q$. In this formulation the parameter $q$ characterizes some specific form of local equilibrium which is characteristic for the nonextensive thermodynamics and which replaces the usual local thermal equilibrium assumption of the usual hydrodynamical models. We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics. It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, $\zeta/s$ and $\eta/s$, to be made.Comment: Final version accepted for publication in Phys. Rev.