355 research outputs found
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 and weak
coupling . 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 . The free energy is separated into the contributions
from the momentum scales and , respectively. The first term can be
written as a perturbation series in . If all forces are screened at the
scale , the second term can be calculated as a perturbation series in
beginning at order . The parameters of the effective theory satisfy
renormalization group equations that can be used to sum up leading logarithms
of . We apply this method to a massless scalar field with a
interaction, calculating the free energy to order and the
screening mass to order .Comment: 40 pages, LaTeX, 5 uuecoded figure
Solution to the 3-loop -derivable Approximation for Scalar Thermodynamics
We solve the 3-loop -derivable approximation to the thermodynamics of
the massless field theory by reducing it to a 1-parameter variational
problem. The thermodynamic potential is expanded in powers of and ,
where is the coupling constant, is a variational mass parameter, and
is the temperature. There are ultraviolet divergences beginning at 6th
order in that cannot be removed by renormalization. However the finite
thermodynamic potential obtained by truncating after terms of 5th order in
and 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
A complete calculation of the finite temperature effective potential for the
abelian Higgs model to the order 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
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- 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
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