Medley in finite temperature field theory

I discuss three subjects in thermal field theory: why in \sun gauge theories the \zn symmetry is broken at high (instead of low) temperature, the possible singularity structure of gauge variant propagators, and the problem of how to compute the viscosity from the Kubo formula.Comment: LaTeX file, 11 pages, BNL-P-2/92 (December, 1992

Gauge invariance of the color-superconducting gap on the mass shell

The gap parameter for color superconductivity is expected to be a gauge invariant quantity, at least on the appropriate mass shell. Computing the gap to subleading order in the QCD coupling constant, g, we show that the prefactor of the exponential in 1/g is gauge dependent off the mass shell, and independent of gauge on the mass shell.Comment: 8 pages, Proceedings of the Conference on Statistical QCD, Bielefeld, August 26 - 30, 200

Color superconductivity in cold, dense quark matter

We review what is different and what is similar in a color superconductor as compared to an ordinary BCS superconductor. The parametric dependence of the zero-temperature gap on the coupling constant differs in QCD from that in BCS theory. On the other hand, the transition temperature to the superconducting phase is related to the zero-temperature gap in the same way in QCD as in BCS theory.Comment: 11 pages, 1 figure, proceedings of the "Fifth Workshop on QCD", Villefranche, Jan. 3-7, 200

Gauge Dependence of the Resummed Thermal Gluon Self Energy

The gauge dependence of the hot gluon self energy is examined in the context of Pisarski's method for resumming hard thermal loops. Braaten and Pisarski have used the Ward identities satisfied by the hard corrections to the n-point functions to argue the gauge fixing independence of the leading order resummed QCD plasma damping rate in covariant and strict Coulomb gauges. We extend their analysis to include all linear gauges that preserve rotational invariance and display explicitly the conditions required for gauge fixing independence. It is shown that in covariant gauges the resummed damping constant is gauge fixing independent only if an infrared regulator is explicitly maintained throughout the calculation.Comment: 29 pages, report BI-TP 92/19, LPTHE-Orsay 92/32, WIN-TH-92/02 (June 1992

Numerical simulation of random paths with a curvature dependent action

We study an ensemble of closed random paths, embedded in R^3, with a curvature dependent action. Previous analytical results indicate that there is no crumpling transition for any finite value of the curvature coupling. Nevertheless, in a high statistics numerical simulation, we observe two different regimes for the specific heat separated by a rather smooth structure. The analysis of this fact warns us about the difficulties in the interpretation of numerical results obtained in cases where theoretical results are absent and a high statistics simulation is unreachable. This may be the case of random surfaces.Comment: 9 pages, LaTeX, 4 eps figures. Final version to appear in Mod. Phys. Lett.

Damping Rate of a Yukawa Fermion at Finite Temperature

The damping of a massless fermion coupled to a massless scalar particle at finite temperature is considered using the Braaten-Pisarski resummation technique. First the hard thermal loop diagrams of this theory are extracted and effective Green's functions are constructed. Using these effective Green's functions the damping rate of a soft Yukawa fermion is calculated. This rate provides the most simple example for the damping of a soft particle. To leading order it is proportional to $g^2T$, whereas the one of a hard fermion is of higher order.Comment: 5 pages, REVTEX, postscript figures appended, UGI-94-0

Application of a multi-site mean-field theory to the disordered Bose-Hubbard model

We present a multi-site formulation of mean-field theory applied to the disordered Bose-Hubbard model. In this approach the lattice is partitioned into clusters, each isolated cluster being treated exactly, with inter-cluster hopping being treated approximately. The theory allows for the possibility of a different superfluid order parameter at every site in the lattice, such as what has been used in previously published site-decoupled mean-field theories, but a multi-site formulation also allows for the inclusion of spatial correlations allowing us, e.g., to calculate the correlation length (over the length scale of each cluster). We present our numerical results for a two-dimensional system. This theory is shown to produce a phase diagram in which the stability of the Mott insulator phase is larger than that predicted by site-decoupled single-site mean-field theory. Two different methods are given for the identification of the Bose glass-to-superfluid transition, one an approximation based on the behaviour of the condensate fraction, and one of which relies on obtaining the spatial variation of the order parameter correlation. The relation of our results to a recent proposal that both transitions are non self-averaging is discussed.Comment: Accepted for publication in Physical Review

Dynamical Locking of the Chiral and the Deconfinement Phase Transition in QCD

We study the fixed-point structure of four-fermion interactions in two-flavor QCD with Nc colors close to the finite-temperature phase boundary. In particular, we analyze how the fixed-point structure of four-fermion interactions is related to the confining dynamics in the gauge sector. We show that there exists indeed a mechanism which dynamically locks the chiral phase transition to the deconfinement phase transition. This mechanism allows us to determine a window for the values of physical observables in which the two phase transitions lie close to each other.Comment: 14 pages, 5 figure