78 research outputs found

### Resummation in hot field theories

We consider a scalar theory at finite temperature in the 2PI resummation
scheme, including phi^3 and phi^4 interactions. Already at the one loop level
in this scheme, we have to deal with a non local approximation. We carry out
the renormalization and obtain finite equations for the propagator. Within this
model we can explore the effect of non local contributions to the self-energy
in the evaluation of thermodynamic quantities.Comment: 5 pages, 3 figures, contribution to the conference Strong and
Electroweak Matter (SEWM2002), Heidelberg, Germany, October 2-5, 200

### Renormalization and gauge symmetry for 2PI effective actions

We explore a method to recover symmetry identities in the 2PI formalism. It
is based on non-perturbative approximations to the 1PI effective action. We
discuss renormalization questions raised by this technique.Comment: 5 pages, 3 figures. To appear in the conference proceedings of Strong
Electroweak Matter 2004 (SEWM04), Helsinki, Finland. 16-19 Jun 200

### Renormalization out of equilibrium in a superrenormalizable theory

We discuss the renormalization of the initial value problem in Nonequilibrium
Quantum Field Theory within a simple, yet instructive, example and show how to
obtain a renormalized time evolution for the two-point functions of a scalar
field and its conjugate momentum at all times. The scheme we propose is
applicable to systems that are initially far from equilibrium and compatible
with non-secular approximation schemes which capture thermalization. It is
based on Kadanoff-Baym equations for non-Gaussian initial states, complemented
by usual vacuum counterterms. We explicitly demonstrate how various
cutoff-dependent effects peculiar to nonequilibrium systems, including
time-dependent divergences or initial-time singularities, are avoided by taking
an initial non-Gaussian three-point vacuum correlation into account.Comment: 5 pages, 2 figure

### Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation

We discuss the thermodynamics of the O(N) model across the corresponding
phase transition using the two-loop Phi-derivable approximation of the
effective potential and compare our results to those obtained in the literature
within the Hartree-Fock approximation. In particular, we find that in the
chiral limit the transition is of the second order, whereas it was found to be
of the first order in the Hartree-Fock case. These features are manifest at the
level of the thermodynamical observables. We also compute the thermal sigma and
pion masses from the curvature of the effective potential. In the chiral limit,
this guarantees that the Goldstone's theorem is obeyed in the broken phase. A
realistic parametrization of the model in the N=4 case, based on the vacuum
values of the curvature masses, shows that a sigma mass of around 450 MeV can
be obtained. The equations are renormalized after extending our previous
results for the N=1 case by means of the general procedure described in [J.
Berges et al., Annals Phys. 320, 344-398 (2005)]. When restricted to the
Hartree-Fock approximation, our approach reveals that certain problems raised
in the literature concerning the renormalization are completely lifted.
Finally, we introduce a new type of Phi-derivable approximation in which the
gap equation is not solved at the same level of accuracy as the accuracy at
which the potential is computed. We discuss the consistency and applicability
of these types of "hybrid" approximations and illustrate them in the two-loop
case by showing that the corresponding effective potential is renormalizable
and that the transition remains of the second order.Comment: 26 pages, 9 figures, uses RevTeX4-1, published versio

### Pad\'e approximants and analytic continuation of Euclidean Phi-derivable approximations

We investigate the Pad\'e approximation method for the analytic continuation
of numerical data and its ability to access, from the Euclidean propagator,
both the spectral function and part of the physical information hidden in the
second Riemann sheet. We test this method using various benchmarks at zero
temperature: a simple perturbative approximation as well as the two-loop
Phi-derivable approximation. The analytic continuation method is then applied
to Euclidean data previously obtained in the O(4) symmetric model (within a
given renormalization scheme) to assess the difference between zero-momentum
and pole masses, which is in general a difficult question to answer within
nonperturbative approaches such as the Phi-derivable expansion scheme.Comment: 20 pages, 8 figures, uses RevTeX 4-

### Loss of solution in the symmetry improved Phi-derivable expansion scheme

We consider the two-loop Phi-derivable approximation for the O(2)-symmetric
scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis
and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's
theorem in the broken phase. Although the corresponding equations admit a
solution in the presence of a large enough infrared (IR) regulating scale, we
argue that, for smooth ultraviolet (UV) regulators, the solution is lost when
the IR scale becomes small enough. Infrared regular solutions exist for certain
non-analytic UV regulators, but we argue that these solutions are artifacts
which should disappear when the sensitivity to the UV regulator is removed by a
renormalization procedure. The loss of solution is observed both at zero and at
finite temperature, although it is simpler to identify in the latter case. We
also comment on possible ways to cure this problem.Comment: 20 pages, 7 figures, uses elsarticle, published versio

### The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite
temperature within the Phi-derivable expansion scheme to order lambda^2. In
continuation to an earlier work, we look for a physical parametrization in the
N=4 case that allows to accommodate the lightest mesons. Using zero-momentum
curvature masses to approximate the physical masses, we find that, in the
parameter range where a relatively large sigma mass is obtained, the scale of
the Landau pole is lower compared to that obtained in the two-loop truncation.
This jeopardizes the insensitivity of the observables to the ultraviolet
regulator and could hinder the predictivity of the model. Both in the N=1 and
N=4 cases, we also find that, when approaching the chiral limit, the
(iterative) solution to the Phi-derivable equations is lost in an interval
around the would-be transition temperature. In particular, it is not possible
to conclude at this order of truncation on the order of the transition in the
chiral limit. Because the same issue could be present in other approaches, we
investigate it thoroughly by considering a localized version of the
Phi-derivable equations, whose solution displays the same qualitative features,
but allows for a more analytical understanding of the problem. In particular,
our analysis reveals the existence of unphysical branches of solutions which
can coalesce with the physical one at some temperatures, with the effect of
opening up a gap in the admissible values for the condensate. Depending on its
rate of growth with the temperature, this gap can eventually engulf the
physical solution.Comment: 26 pages, 15 figures, uses RevTeX4-1, published versio

### A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations

We revisit the renormalization of Phi-derivable approximations from a
slightly different point of view than the one which is usually followed in
previous works. We pay particular attention to the question of the existence of
a solution to the self-consistent equation that defines the two-point function
in the Cornwall-Jackiw-Tomboulis formalism and to the fact that some of the
ultraviolet divergences which appear if one formally expands the solution in
powers of the bare coupling do not always appear as divergences at the level of
the solution itself. We discuss these issues using a particular truncation of
the Phi functional, namely the simplest truncation which brings non-trivial
momentum and field dependence to the two-point function.Comment: 30 pages, 12 figure

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