arXiv subjects

Michael C. Ogilvie

Publications and source records attributed to Michael C. Ogilvie.

At least 73 records · Page 4Linked to original sources

arXiv2000

Spinodal Decomposition in High Temperature Gauge Theories

After a rapid increase in temperature across the deconfinement temperature $% T_{d}$, pure gauge theories exhibit unstable long wavelength fluctuations in the approach to equilibrium. This phenomenon is analogous to spinodal decomposition observed in condensed matter physics, and also seen in models of disordered chiral condensate formation. At high temperature, the unstable modes occur only in the range $0\leq k$ $\leq k_{c}$, where $k_{c}$ is on the order of the Debye screening mass $m_D$. Equilibration always occurs via spinodal decomposition for $SU(2) $at temperatures $T>T_{d}$ and for SU(3) for $T\gg T_{d}$. For SU(3) at temperatures $T\gtrsim T_{d}$, nucleation may replace spinodal decomposition as the dominant equilibration mechanism. Monte Carlo simulations of SU(2) lattice gauge theory exhibit the predicted phenomena. The observed value of $k_c$ is in reasonable agreement with a value predicted from previous lattice measurements of $m_D$.

hep-lat↗

arXiv1999

Landau-Ginsberg Theory of Quark Confinement

We describe the SU(3) deconfinement transition using Landau-Ginsberg theory. Drawing on perturbation theory and symmetry principles, we construct the free energy as a function of temperature and the Polyakov loop. Once the two adjustable parameters of the model are fixed, the pressure p, energy epsilon and Polyakov loop expectation value P_F are calculable functions of temperature. An excellent fit to the continuum extrapolation of lattice thermodynamics data can be achieved. In an extended form of the model, the glueball potential is responsible for breaking scale invariance at low temperatures. Three parameters are required, but the glueball mass and the gluon condensate are calculable functions of temperature, along with p, epsilon and P_F.

hep-lat↗

arXiv1998

Theory of Abelian Projection

Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The methods used emphasize that the projected theory is derived from the underlying non-Abelian theory rather than vice versa. In general, the choice of subgroup used for projection is not very important, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements. Two other issues, Casimir scaling and the conflict between projection and critical universality, are also discussed.

hep-lat↗

arXiv1998

A First Principles Estimate of Finite Size Effects in Quark-Gluon Plasma Formation

Using lattice simulations of quenched QCD we estimate the finite size effects present when a gluon plasma equilibrates in a slab geometry, i.e., finite width but large transverse dimensions. Significant differences are observed in the free energy density for the slab when compared with bulk behavior. A small shift in the critical temperature is also seen. The free energy required to liberate heavy quarks relative to bulk is measured using Polyakov loops; the additional free energy required is on the order of 30-40 MeV at 2-3 T_c.

hep-lat↗

arXiv1998

Analytical Results for Abelian Projection

Analytic methods for Abelian projection are developed, and a number of results related to string tension measurements are obtained. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The subgroup used for projection need only contain the center of the gauge group, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements.

hep-lat↗

arXiv1998

Finite Size Effects in Quark-Gluon Plasma Formation

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arXiv1998

Monte Carlo Estimate of Finite Size Effects in Quark-Gluon Plasma Formation

hep-ph↗

arXiv1997

Non-Perturbative Evaluation of the Physical Classical Velocity in the Lattice Heavy Quark Effective Theory

In the lattice formulation of the Heavy Quark Effective Theory, the value of the classical velocity v, as defined through the separation of the 4-momentum of a heavy quark into a part proportional to the heavy quark mass and a residual part which remains finite in the heavy quark limit (P = Mv + p) is different from its value as it appears in the bare heavy quark propagator (S(p) = 1/vp). The origin of the difference, which is effectively a lattice-induced renormalization, is the reduction of Lorentz (or O(4)) invariance to (hyper)-cubic invariance. The renormalization is finite and depends specifically on the form of the discretization of the reduced heavy quark Dirac equation. For the Forward Time - Centered Space discretization, we compute this renormalization non-perturbatively, using an ensemble of lattices at beta = 6.1 provided by the Fermilab ACP-MAPS Collaboration. The calculation makes crucial use of a variationally optimized smeared operator for creating composite heavy-light mesons. It has the property that its propagator achieves an asymptotic plateau in just a few Euclidean time steps. For comparison, we also compute the shift perturbatively, to one loop in lattice perturbation theory. The non-perturbative calculation of the leading multiplicative shift in the classical velocity is considerably different from the one-loop estimate, and indicates that for the above parameters, v is reduced by about 10-13%.

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arXiv1997

Finite Temperature Quark Confinement

Confinement may be more easily demonstrated at finite temperature using the Polyakov loop than at zero temperature using the Wilson loop. A natural mechanism for confinement can arise via the coupling of the adjoint Polyakov loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation of the effective potential for SU(2) gluons in a background field consisting of a non-zero color magnetic field and a non-trivial Polyakov loop. The color magnetic field drives the Polyakov loop to non-trivial behavior, and the Polyakov loop can remove the well-known tachyonic mode associated with the Saviddy vacuum. Minimizing the real part of the effective potential leads to confinement, as determined by the Polyakov loop. Unfortunately, we cannot arrange for simultaneous stability and confinement for this simple class of field configurations. We show for a large class of abelian background fields that at one loop tachyonic modes are necessary for confinement.

hep-lat↗

arXiv1996

Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity

We discuss the renormalization of the lattice formulation of the Heavy Quark Effective Theory (LHQET). In addition to wave function and composite operator renormalizations, on the lattice the classical velocity is also renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. We present results of a new, direct lattice simulation of this finite renormalization, and compare the results to the perturbative (one loop) result. The simulation results are obtained with the use of a variationally optimized heavy-light meson operator, using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.

hep-lat↗

arXiv1996

Renormalization of the Classical Velocity in the Lattice Heavy Quark Effective Theory

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the classical velocity becomes renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite, depends on the form of the discretization of the reduced heavy quark Dirac equation, and can persist down to zero lattice spacing. For the Forward Time - Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using an ensemble of lattices provided by the Fermilab ACP-MAPS collaboration. The estimates of the leading multiplicative shift agree reasonably well, and indicate that to first order, the classical velocity is reduced by about 20-25%.

hep-lat↗

arXiv1995

Chiral Symmetry Restoration and $Z_N$ Symmetry

We demonstrate that chiral symmetry restoration in quenched finite temperature QCD depends crucially on the $Z_3$ phase of the Polyakov loop ${\cal P}$. This dependence is a general consequence of the coupling of the chiral order parameter to the Polyakov loop. We construct a model for chiral symmetry breaking and restoration which includes the effect of a nontrivial Polyakov loop by calculating the effective potential for the chiral condensate of a Nambu-Jona-Lasinio model in a uniform temperature dependent $A_0$ gauge field background. Above the deconfinement temperature there are three possible phases corresponding to the $Z_3$ symmetric phases of the Polyakov loop in the pure gauge theory. In the phase in which ${\rm tr_c}({\cal P})$ is real and positive the first order deconfining transition induces chiral symmetry restoration in agreement with simulation results. In the two phases where $Re[{\rm tr_c}({\cal P})] < 0$ the sign of the leading finite temperature correction to the effective potential is reversed from the normal phase, and chiral symmetry is not restored at the deconfinement transition; this agrees with the recent simulation studies of Chandrasekharan and Christ. In the case of $SU(N)$ a rich set of possibilites emerges. The generality of the mechanism makes it likely to occur in full QCD as well; this will increase the lifetimes of metastable $Z_3$ phases.

hep-lat↗

arXiv1995

Renormalization of the Lattice Heavy Quark Classical Velocity

In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the classical velocity is renormalized. The origin of this renormalization is the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The renormalization is finite and depends on the form of the decretization of the reduced heavy quark Dirac equation. For the Forward Time - Centered Space discretization, the renormalization is computed both perturbatively, to one loop, and non-perturbatively using an ensemble of lattices provided by the Fermilab lattice collaboration. The estimates of the leading (linear) shift agree, and indicate that for small classical velocities, the renormalized velocity is reduced by about 25-30% relative to its bare (input) value.

hep-lat↗

arXiv1995

Coupling the Deconfining and Chiral Transitions

The Polyakov loop and the chiral condensate are used as order parameters to explore analytically the possible phase structure of finite temperature QCD. Nambu-Jona-Lasinio models in a background temporal gauge field are combined with a Polyakov loop potential in a form suitable for both the lattice and the continuum. Three possible behaviors are found: a first-order transition, a second-order transition, and a region with both transitions.

hep-lat↗

arXiv1995

An Effective Action for Finite Temperature Lattice Gauge Theories with Dynamical Fermions

Dynamical fermions induce via the fermion determinant a gauge-invariant effective action. In principle, this effective action can be added to the usual gauge action in simulations, reproducing the effects of closed fermion loops. Using lattice perturbation theory at finite temperature, we compute for staggered fermions the one-loop fermionic corrections to the spatial and temporal plaquette couplings as well as the leading $Z_N$ symmetry breaking coupling. A. Hasenfratz and T. DeGrand have shown that $β_c$ for dynamical staggered fermions can be accurately estimated by the formula $β_c = β^{\rm pure}_c - Δβ_F$ where $Δβ_F$ is the shift induced by the fermions at zero temperature. Numerical and analytical results indicate that the finite temperature corrections to the zero-temperature calculation of A. Hasenfratz and T. DeGrand are small for small values of $κ= {1\over 2m_F}$, but become significant for intermediate values of $κ$. The effect of these finite temperature corrections is to ruin the agreement of the Hasenfratz-DeGrand calculation with Monte Carlo data. We argue, however, that the finite temperature corrections are suppressed nonperturbatively at low temperatures, resolving this apparent disagreement. The $Z_N$ symmetry breaking coupling is small; we argue that it changes the order of the transition while having little effect on the critical value of $β$.

hep-lat↗

arXiv1994

An Effective Action for Finite Temperature QCD with Fermions

Using lattice perturbation theory at finite temperature, we compute for staggered fermions the one-loop fermionic corrections to the spatial and temporal plaquette couplings as well as the leading $Z_N$ symmetry breaking coupling. Numerical and analytical considerations indicate that the finite temperature corrections to the zero-temperature calculation of A. Hasenfratz and T. DeGrand are small for small values of $κ= {1\over 2m_F}$, but become significant for intermediate values of $κ$. The effect of these finite temperature corrections is to ruin the agreement of the Hasenfratz-DeGrand calculation with Monte Carlo data. We conjecture that the finite temperature corrections are suppressed nonperturbatively at low temperatures, resolving this apparent disagreement. The $Z_N$ symmetry breaking coupling is small; we argue that it may change the order of the transition while having little effect on the critical value of $β$.

hep-lat↗

arXiv1994

Finite Temperature QCD Interfaces Out of Equilibrium

The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface terms induced in effective actions by abrupt temperature changes provide a natural theoretical framework for understanding the occurence of both continuous and discontinuous behavior in the order parameter. Monte Carlo simulation of pure QCD shows both kinds of interfacial behavior. Perturbation theory predicts a universal profile in the high temperature phase, which can be tested by Monte Carlo simulation.

hep-lat↗

arXiv1994

Structural Properties of the Lattice Heavy Quark Effective Theory

We discuss two related aspects of the lattice version of the heavy quark effective theory (HQET). They are the effects of heavy quark modes with large momenta, near the boundary of the Brillouin zone, and the renormalization of the lattice HQET. We argue that even though large momentum modes are present, their contributions to heavy-light bound states and perturbative loop integrals are dynamically suppressed and vanish in the continuum limit. We also discuss a new feature of the renormalization of the lattice HQET not present in the continuum theory, namely that the classical velocity is finitely renormalized.

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