Eliminating Infrared Divergences in the Pressure

The pressure of a system in thermal equilibrium is expressed as a mass integral over a sum of thermal propagators. This allows a Dyson resummation and is used to demonstrate that potential infrared divergences are rendered harmless.Comment: 6 pages plain tex, including figures embedded using eps

The Massive Thermal Basketball Diagram

The "basketball diagram" is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a phi^4 interaction to three-loop order.Comment: 19 pages, 3 figure

Effective Field Theory Approach to High-Temperature Thermodynamics

An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional reduction to the bosonic zero-frequency modes. The parameters of the effective theory can be calculated as perturbation series in the running coupling constant $g^2(T)$. The free energy is separated into the contributions from the momentum scales $T$ and $gT$, respectively. The first term can be written as a perturbation series in $g^2(T)$. If all forces are screened at the scale $gT$, the second term can be calculated as a perturbation series in $g(T)$ beginning at order $g^3$. The parameters of the effective theory satisfy renormalization group equations that can be used to sum up leading logarithms of $T/(gT)$. We apply this method to a massless scalar field with a $\Phi^4$ interaction, calculating the free energy to order $g^6 \log g$ and the screening mass to order $g^5 \log g$.Comment: 40 pages, LaTeX, 5 uuecoded figure

Solution to the 3-loop Φ\Phi-derivable Approximation for Scalar Thermodynamics

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless $\phi^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.Comment: 4 pages, 1 figur

Finite Temperature Effective Potential for the Abelian Higgs Model to the Order e4,λ2e^4,\lambda^2

A complete calculation of the finite temperature effective potential for the abelian Higgs model to the order $e^4,\lambda^2$ is presented and the result is expressed in terms of physical parameters defined at zero temperature. The absence of a linear term is verified explicitly to the given order and proven to survive to all orders. The first order phase transition has weakened in comparison with lower order calculation, which shows up in a considerable decrease of the surface tension. The only difference from the original version is the splitting of some overlong lines causing problems with certain mailers.Comment: 13 pages LaTex ( figures not included , hardcopy available on request : [email protected] or t00heb@dhhdesy3 ) , DESY 93-08

Transport coefficients, spectral functions and the lattice

Transport coefficients are determined by the slope of spectral functions of composite operators at zero frequency. We study the spectral function relevant for the shear viscosity for arbitrary frequencies in weakly-coupled scalar and nonabelian gauge theories at high temperature and compute the corresponding correlator in euclidean time. We discuss whether nonperturbative values of transport coefficients can be extracted from euclidean lattice simulations.Comment: 25 pages with 7 eps figures, discussion improved, acknowledgement added; to appear in JHE

Resummation Methods at Finite Temperature: The Tadpole Way

We examine several resummation methods for computing higher order corrections to the finite temperature effective potential, in the context of a scalar $\phi^4$ theory. We show by explicit calculation to four loops that dressing the propagator, not the vertex, of the one-loop tadpole correctly counts ``daisy'' and ``super-daisy'' diagrams.Comment: 18 pages, LaTeX, CALT-68-1858, HUTP-93-A011, EFI-93-2

The pressure of hot QCD up to g^6 ln(1/g)

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order g^5. We compute here the last contribution which can be determined perturbatively, g^6 ln(1/g), by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative g^6 ln(1/g) terms, once they are summed together with the so far unknown perturbative and non-perturbative g^6 terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.Comment: 18 pages. Small clarifications added. To appear in Phys.Rev.

Foam Diagram Summation at Finite Temperature

We show that large-$N$ $\phi ^4$ theory is not trivial if one accepts the presence of a tachyon with a truly huge mass, and that it allows exact calculation. We use it to illustrate how to calculate the exact resummed pressure at finite temperature and verify that it is infrared and ultraviolet finite even in the zero-mass case. In 3 dimensions a residual effect of the resummed infrared divergences is that at low temperature or strong coupling the leading term in the interaction pressure becomes independent of the coupling and is 4/5 of the free-field pressure. In 4 dimensions the pressure is well-defined provided that the temperature is below the tachyon mass. We examine how rapidly this expansion converges and use our analysis to suggest how one might reorganise perturbation theory to improve the calculation of the pressure for the QCD plasma.Comment: 18 pages plain tex, with 8 figures embedded with epsf. Equation (2.15) has been corrected and the consequent changes made to the figures. A further analytic result has been added to the 3-dimensional calculatio

Shear viscosity of hot scalar field theory in the real-time formalism

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called (r,a) basis. The general result is applied to scalar field theory with pure lambda*phi**4 and mixed g*phi**3+lambda*phi**4 interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.Comment: Expanded introduction and conclusions. Several references and a footnote added. Fig.5 and its discussion in the text modified to avoid double counting. Signs in Eqs. (45) and (53) correcte