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

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

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.

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

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

On the Perturbative Nature of Color Superconductivity

Color superconductivity is a possible phase of high density QCD. We present a systematic derivation of the transition temperature, T_C, from the QCD Lagrangian through study of the di-quark proper vertex. With this approach, we confirm the dependence of T_C on the coupling g, namely $T_C \sim \mu g^{-5} e^{-\kappa/g}$, previously obtained from the one-gluon exchange approximation in the superconducting phase. The diagrammatic approach we employ allows us to examine the perturbative expansion of the vertex and the propagators. We find an additional O(1) contribution to the prefactor of the exponential from the one-loop quark self energy and that the other one-loop radiative contributions and the two gluon exchange vertex contribution are subleading.Comment: 13 pages, 3 figures, revtex, details and discussion expande

Soft Photon Production Rate in Resummed Perturbation Theory of High Temperature QCD

We calculate the production rate of soft real photons from a hot quark -- gluon plasma using Braaten -- Pisarski's perturbative resummation method. To leading order in the QCD coupling constant $g$ we find a logarithmically divergent result for photon energies of order $gT$, where $T$ is the plasma temperature. This divergent behaviour is due to unscreened mass singularities in the effective hard thermal loop vertices in the case of a massless external photon.Comment: 13 pages (2 figures not included), PLAINTEX, LPTHE-Orsay 93/46, BI-TP 93/5

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