62 research outputs found
Self-consistent bounces in two dimensions
We compute bounce solutions describing false vacuum decay in a Phi**4 model
in two dimensions in the Hartree approximation, thus going beyond the usual
one-loop corrections to the decay rate. We use zero energy mode functions of
the fluctuation operator for the numerical computation of the functional
determinant and the Green's function. We thus avoid the necessity of
discretizing the spectrum, as it is necessary when one uses numerical
techniques based on eigenfunctions. Regularization is performed in analogy of
standard perturbation theory; the renormalization of the Hartree approximation
is based on the two-particle point-irreducible (2PPI) scheme. The iteration
towards the self-consistent solution is found to converge for some range of the
parameters. Within this range we find the corrections to the leading one-loop
approximation to be relatively small, not exceeding one order of magnitude in
the total transition rate.Comment: 30 pages, 12 figure
One-loop corrections to the metastable vacuum decay
We evaluate the one-loop prefactor in the false vacuum decay rate in a theory
of a self interacting scalar field in 3+1 dimensions. We use a numerical
method, established some time ago, which is based on a well-known theorem on
functional determinants. The proper handling of zero modes and of
renormalization is discussed. The numerical results in particular show that
quantum corrections become smaller away from the thin-wall case. In the
thin-wall limit the numerical results are found to join into those obtained by
a gradient expansion.Comment: 31 pages, 7 figure
Nonequilibrium dynamics: a renormalized computation scheme
We present a regularized and renormalized version of the one-loop nonlinear
relaxation equations that determine the non-equilibrium time evolution of a
classical (constant) field coupled to its quantum fluctuations. We obtain a
computational method in which the evaluation of divergent fluctuation integrals
and the evaluation of the exact finite parts are cleanly separated so as to
allow for a wide freedom in the choice of regularization and renormalization
schemes. We use dimensional regularization here. Within the same formalism we
analyze also the regularization and renormalization of the energy-momentum
tensor. The energy density serves to monitor the reliability of our numerical
computation. The method is applied to the simple case of a scalar phi^4 theory;
the results are similar to the ones found previously by other groups.Comment: 15 pages, 9 postscript figures, revtex; version published in Phys.
Rev, with minor corrections; improves the first version of 1996 by including
the discussion of energy momentum tenso
The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N
We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI
formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective
potential at finite temperature. At next-to-leading order in a 1/N expansion
one has to include the sums over "necklace" and generalized "sunset" diagrams.
We find that - in contrast to the Hartree approximation - there is no
spontaneous symmetry breaking in this approximation, as to be expected for the
exact theory. The effective potential becomes convex throughout for all
parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and
temperatures between 0.2 and 1. The Green's functions obtained by solving the
Schwinger-Dyson equations are enhanced in the infrared region. We also compare
the effective potential as function of the external field phi with those
obtained in various other approximations.Comment: 19 pages, 9 figures; v2: references added, some changes in the tex
Nonequilibrium dynamics: preheating in the SU(2) Higgs model
The term `preheating' has been introduced recently to denote the process in
which energy is transferred from a classical inflaton field into fluctuating
field (particle) degrees of freedom without generating yet a real thermal
ensemble. The models considered up to now include, besides the inflaton field,
scalar or fermionic fluctuations. On the other hand the typical ingredient of
an inflationary scenario is a nonabelian spontaneously broken gauge theory. So
the formalism should also be developed to include gauge field fluctuations
excited by the inflaton or Higgs field. We have chosen here, as the simplest
nonabelian example, the SU(2) Higgs model. We consider the model at temperature
zero. From the technical point of view we generalize an analytical and
numerical renormalized formalism developed by us recently to coupled channnel
systems. We use the 't Hooft-Feynman gauge and dimensional regularization. We
present some numerical results but reserve a more exhaustive discussion of
solutions within the paramter space of two couplings and the initial value of
the Higgs field to a future publication.Comment: 30 pages, 10 figures in enhanced postscript, 2 unreadable figures
made accessibl
Out-of-equilibrium evolution of scalar fields in FRW cosmology: renormalization and numerical simulations
We present a renormalized computational framework for the evolution of a
self-interacting scalar field (inflaton) and its quantum fluctuations in an FRW
background geometry. We include a coupling of the field to the Ricci scalar
with a general coupling parameter . We take into account the classical and
quantum back reactions, i.e., we consider the the dynamical evolution of the
cosmic scale factor. We perform, in the one-loop and in the large-N
approximation, the renormalization of the equation of motion for the inflaton
field, and of its energy momentum tensor. Our formalism is based on a
perturbative expansion for the mode functions, and uses dimensional
regularization. The renormalization procedure is manifestly covariant and the
counter terms are independent of the initial state. Some shortcomings in the
renormalization of the energy-momentum tensor in an earlier publication are
corrected. We avoid the occurence of initial singularities by constructing a
suitable class of initial states. The formalism is implemented numerically and
we present some results for the evolution in the post-inflationary preheating
era.Comment: 44 pages, uses latexsym, 6 pages with 11 figures in a .ps fil
Parton distributions in the chiral quark model: a continuum computation
We compute the parton distributions for the chiral quark model. We present a
new technique for performing such computations based on Green functions. This
approach avoids a discretization of the spectrum. It therefore does not need
any smoothing procedures.
The results are similar to those of other groups, however the distributions
peak at smaller .Comment: 19 pages, 8 Figures, LaTeX, some typos corrected, some additional
comments in the conclusion
One-loop corrections to the Nielsen-Olesen vortex: finite length
We consider the one-loop quantum corrections to the Nielsen-Olesen flux tube
of finite length , by imposing periodic boundary conditions. The
calculations are based on a recent evaluation of these quantum corrections to
the string tension of an infinite vortex. The finite length corrections are
finite from the outset. If the computation is restricted to the zero modes we
obtain the standard L\"uscher term for a closed string. The inclusion
of the other fluctuation modes of Higgs and gauge fields, using the numerically
computed trace of the Euclidian Green's function, leads to corrections that
decrease exponentially with . We present numerical results for these
corrections, discuss their possible relevance, and the limitations of the
approach.Comment: 15 pages, 5 figure
Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking
We consider the out-of-equilibrium evolution of a classical condensate field
and its quantum fluctuations for a scalar O(N) model with spontaneously broken
symmetry. In contrast to previous studies we do not consider the large N limit,
but the case of finite N, including N=1, i.e., plain theory.
The instabilities encountered in the one-loop approximation are prevented, as
in the large-N limit, by back reaction of the fluctuations on themselves, or,
equivalently, by including a resummation of bubble diagrams.
For this resummation and its renormalization we use formulations developed
recently based on the effective action formalism of Cornwall, Jackiw and
Tomboulis. The formulation of renormalized equations for finite N derived here
represents a useful tool for simulations with realistic models. Here we
concentrate on the phase structure of such models. We observe the transition
between the spontaneously broken and the symmetric phase at low and high energy
densities, respectively. This shows that the typical structures expected in
thermal equilibrium are encountered in nonequilibrium dynamics even at early
times, i.e., before an efficient rescattering can lead to thermalization.Comment: 31 pages, 19 Figures, LaTeX; extended discussion on the basis of:
fluctuations, eff. potential, correlations, analytic calculation of
parametric resonance for "pion"_and_ "sigma" field
Renormalization of the nonequilibrium dynamics of fermions in a flat FRW universe
We derive the renormalized equations of motion and the renormalized
energy-momentum tensor for fermions coupled to a spatially homogeneous scalar
field (inflaton) in a flat FRW geometry. The fermion back reaction to the
metric and to the inflaton field is formulated in one-loop approximation.
Having determined the infinite counter terms in an scheme we
formulate the finite terms in a form suitable for numerical computation. We
comment on the trace anomaly which is inferred from the standard analysis. We
also address the problem of initial singularities and determine the Bogoliubov
transformation by which they are removed.Comment: 26 pages, LaTe
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