Resummations in Hot Scalar Electrodynamics

The gauge-boson sector of perturbative scalar electrodynamics is investigated in detail as a testing ground for resummation methods in hot gauge theories. It also serves as a simple non-trivial reference system for the non-Abelian gluon plasma. The complete next-to-leading order contributions to the polarization tensor are obtained within the resummation scheme of Braaten and Pisarski. The simpler scheme proposed recently by Arnold and Espinosa is shown to apply to static quantities only, whereas Braaten-Pisarski resummation turns out to need modification for collective phenomena close to the light-cone. Finally, a recently proposed resummation of quasi-particle damping contributions is assessed critically.Comment: 53 p. LaTeX, 7 figs. (2 in LaTeX, 5 EPS appended as uu-encoded file), ITP-UH-01/94 & DESY 94-03

Comment on ``High Temperature Fermion Propagator -- Resummation and Gauge Dependence of the Damping Rate''

Baier et al. have reported the damping rate of long-wavelength fermionic excitations in high-temperature QED and QCD to be gauge-fixing-dependent even within the resummation scheme due to Braaten and Pisarski. It is shown that this problem is caused by the singular nature of the on-shell expansion of the fermion self-energy in the infra-red. Its regularization reveals that the alleged gauge dependence pertains to the residue rather than the pole of the fermion propagator, so that in particular the damping constant comes out gauge-independent, as it should.Comment: 5 page

Pressure to order g8∗log(g)g^8*log(g) in ϕ4\phi^4-theory at weak coupling

We calculate the pressure of massless $\phi^4$-theory to order $g^8\log(g)$ at weak coupling. The contributions to the pressure arise from the hard momentum scale of order $T$ and the soft momentum scale of order $gT$. Effective field theory methods and dimensional reduction are used to separate the contributions from the two momentum scales: The hard contribution can be calculated as a power series in $g^2$ using naive perturbation theory with bare propagators. The soft contribution can be calculated using an effective theory in three dimensions, whose coefficients are power series in $g^2$. This contribution is a power series in $g$ starting at order $g^3$. The calculation of the hard part to order $g^6$ involves a complicated four-loop sum-integral that was recently calculated by Gynther, Laine, Schr\"oder, Torrero, and Vuorinen. The calculation of the soft part requires calculating the mass parameter in the effective theory to order $g^6$ and the evaluation of five-loop vacuum diagrams in three dimensions. This gives the free energy correct up to order $g^7$. The coefficients of the effective theory satisfy a set of renormalization group equations that can be used to sum up leading and subleading logarithms of $T/gT$. We use the solutions to these equations to obtain a result for the free energy which is correct to order $g^8\log(g)$. Finally, we investigate the convergence of the perturbative series.Comment: 29 pages and 12 figs. New version: we have pushed the calculations to g^8*log(g) using the renormalization group to sum up log(g) from higher orders. Published in JHE

Real time statistical field theory

We have written a {\it Mathematica} program that calculates the integrand corresponding to any amplitude in the closed-time-path formulation of real time statistical field theory. The program is designed so that it can be used by someone with no previous experience with {\it Mathematica}. It performs the contractions over the tensor indices that appear in real time statistical field theory and gives the result in the 1-2, Keldysh or RA basis. We have used the program to calculate the ward identity for the QED 3-point function, the QED 4-point function for two photons and two fermions, and the QED 5-point function for three photons and two fermions. In real time statistical field theory, there are seven 3-point functions, 15 4-point functions and 31 5-point functions. We produce a table that gives the results for all of these functions. In addition, we give a simple general expression for the KMS conditions between $n$-point green functions and vertex functions, in both the Keldysh and RA basesComment: 25 pages, 12 figure

Dynamics of Quark-Gluon-Plasma Instabilities in Discretized Hard-Loop Approximation

Non-Abelian plasma instabilities have been proposed as a possible explanation for fast isotropization of the quark-gluon plasma produced in relativistic heavy-ion collisions. We study the real-time evolution of these instabilities in non-Abelian plasmas with a momentum-space anisotropy using a hard-loop effective theory that is discretized in the velocities of hard particles. We extend our previous results on the evolution of the most unstable modes, which are constant in directions transverse to the direction of anisotropy, from gauge group SU(2) to SU(3). We also present first full 3+1-dimensional simulation results based on velocity-discretized hard loops. In contrast to the effectively 1+1-dimensional transversely constant modes we find subexponential behaviour at late times.Comment: 30 pages, 16 figures. v3 typos fixe

The pressure of QED from the two-loop 2PI effective action

We compute the pressure of hot quantum electrodynamics from the two-loop truncation of the 2PI effective action. Since the 2PI resummation guarantees gauge-fixing independence only up to the order of the truncation, our result for the pressure presents a gauge dependent contribution of O(e^4). We numerically characterize the credibility of this gauge-dependent calculation and find that the uncertainty due to gauge parameter dependence is under control for xi<1. Our calculation also suggests that the choice of Landau gauge may minimize gauge-dependent effects.Comment: 15 latex pages with 3 figure

Semiclassical thermodynamics of scalar fields

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -- both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -- are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.Comment: 24 pages, 5 postscript figure

Non-perturbative thermal flows and resummations

We construct a functional renormalisation group for thermal fluctuations. Thermal resummations are naturally built in, and the infrared problem of thermal fluctuations is well under control. The viability of the approach is exemplified for thermal scalar field theories. In gauge theories the present setting allows for the construction of a gauge-invariant thermal renormalisation group.Comment: 16 pages, eq (38) added to match published versio

Damping rate of plasmons and photons in a degenerate nonrelativistic plasma

A calculation is presented of the plasmon and photon damping rates in a dense nonrelativistic plasma at zero temperature, following the resummation program of Braaten-Pisarski. At small soft momentum $k$, the damping is dominated by $3 \to 2$ scattering processes corresponding to double longitudinal Landau damping. The dampings are proportional to $(\alpha/v_{F})^{3/2} k^2/m$, where $v_{F}$ is the Fermi velocity.Comment: 9 pages, 2 figure