73 research outputs found
Generalized Boltzmann equations for on-shell particle production in a hot plasma
A novel refinement of the conventional treatment of Kadanoff--Baym equations
is suggested. Besides the Boltzmann equation another differential equation is
used for calculating the evolution of the non-equilibrium two-point function.
Although it was usually interpreted as a constraint on the solution of the
Boltzmann equation, we argue that its dynamics is relevant to the determination
and resummation of the particle production cut contributions. The differential
equation for this new contribution is illustrated in the example of the cubic
scalar model. The analogue of the relaxation time approximation is suggested.
It results in the shift of the threshold location and in smearing out of the
non-analytic threshold behaviour of the spectral function. Possible
consequences for the dilepton production are discussed.Comment: 22 pages, latex, 2 ps figure
Particle Currents in a Space-Time dependent and CP-violating Higgs Background: a Field Theory Approach
Motivated by cosmological applications like electroweak baryogenesis, we
develop a field theoretic approach to the computation of particle currents on a
space-time dependent and CP-violating Higgs background. We consider the
Standard Model model with two Higgs doublets and CP violation in the scalar
sector, and compute both fermionic and Higgs currents by means of an expansion
in the background fields. We discuss the gauge dependence of the results and
the renormalization of the current operators, showing that in the limit of
local equilibrium, no extra renormalization conditions are needed in order to
specify the system completely.Comment: 21 pages, LaTeX file, uses epsf.sty. 4 figures available as a
compressed .ep
Nonequilibrium perturbation theory for complex scalar fields
Real-time perturbation theory is formulated for complex scalar fields away
from thermal equilibrium in such a way that dissipative effects arising from
the absorptive parts of loop diagrams are approximately resummed into the
unperturbed propagators. Low order calculations of physical quantities then
involve quasiparticle occupation numbers which evolve with the changing state
of the field system, in contrast to standard perturbation theory, where these
occupation numbers are frozen at their initial values. The evolution equation
of the occupation numbers can be cast approximately in the form of a Boltzmann
equation. Particular attention is given to the effects of a non-zero chemical
potential, and it is found that the thermal masses and decay widths of
quasiparticle modes are different for particles and antiparticles.Comment: 15 pages using RevTeX; 2 figures in 1 Postscript file; Submitted to
Phys. Rev.
Perturbative nonequilibrium dynamics of phase transitions in an expanding universe
A complete set of Feynman rules is derived, which permits a perturbative
description of the nonequilibrium dynamics of a symmetry-breaking phase
transition in theory in an expanding universe. In contrast to a
naive expansion in powers of the coupling constant, this approximation scheme
provides for (a) a description of the nonequilibrium state in terms of its own
finite-width quasiparticle excitations, thus correctly incorporating
dissipative effects in low-order calculations, and (b) the emergence from a
symmetric initial state of a final state exhibiting the properties of
spontaneous symmetry breaking, while maintaining the constraint . Earlier work on dissipative perturbation theory and spontaneous symmetry
breaking in Minkowski spacetime is reviewed. The central problem addressed is
the construction of a perturbative approximation scheme which treats the
initial symmetric state in terms of the field , while the state that
emerges at later times is treated in terms of a field , linearly related
to . The connection between early and late times involves an infinite
sequence of composite propagators. Explicit one-loop calculations are given of
the gap equations that determine quasiparticle masses and of the equation of
motion for and the renormalization of these equations is
described. The perturbation series needed to describe the symmetric and
broken-symmetry states are not equivalent, and this leads to ambiguities
intrinsic to any perturbative approach. These ambiguities are discussed in
detail and a systematic procedure for matching the two approximations is
described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review
Time evolution in linear response: Boltzmann equations and beyond
In this work a perturbative linear response analysis is performed for the
time evolution of the quasi-conserved charge of a scalar field. One can find
two regimes, one follows exponential damping, where the damping rate is shown
to come from quantum Boltzmann equations. The other regime (coming from
multiparticle cuts and products of them) decays as power law. The most
important, non-oscillating contribution in our model comes from a 4-particle
intermediate state and decays as 1/t^3. These results may have relevance for
instance in the context of lepton number violation in the Early Universe.Comment: 19 page
Real-time propagators at finite temperature and chemical potential
We derive a form of spectral representations for all bosonic and fermionic
propagators in the real-time formulation of field theory at finite temperature
and chemical potential. Besides being simple and symmetrical between the
bosonic and the fermionic types, these representations depend explicitly on
analytic functions only. This last property allows a simple evaluation of loop
integrals in the energy variables over propagators in this form, even in
presence of chemical potentials, which is not possible over their conventional
form
Magnetic field generation from non-equilibrium phase transitions
We study the generation of magnetic fields during the stage of particle
production resulting from spinodal instabilities during phase transitions out
of equilibrium. The main premise is that long-wavelength instabilities that
drive the phase transition lead to strong non-equilibrium charge and current
fluctuations which generate electromagnetic fields. We present a formulation
based on the non-equilibrium Schwinger-Dyson equations that leads to an exact
expression for the spectrum of electromagnetic fields valid for general
theories and cosmological backgrounds and whose main ingredient is the
transverse photon polarization out of equilibrium. This formulation includes
the dissipative effects of the conductivity in the medium. As a prelude to
cosmology we study magnetogenesis in Minkowski space-time in a theory of N
charged scalar fields to lowest order in the gauge coupling and to leading
order in the large N within two scenarios of cosmological relevance. The
long-wavelength power spectrum for electric and magnetic fields at the end of
the phase transition is obtained explicitly.
It follows that equipartition between electric and magnetic fields does not
hold out of equilibrium. In the case of a transition from a high temperature
phase, the conductivity of the medium severely hinders the generation of
magnetic fields, however the magnetic fields generated are correlated on scales
of the order of the domain size, which is much larger than the magnetic
diffusion length. Implications of the results to cosmological phase transitions
driven by spinodal unstabilities are discussed.Comment: Preprint no. LPTHE 02-55, 30 pages, latex, 2 eps figures. Added one
reference. To appear in Phys. Rev.
Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
Within finite temperature field theory, we show that truncated
non-perturbative self-consistent Dyson resummation schemes can be renormalized
with local counter-terms defined at the vacuum level. The requirements are that
the underlying theory is renormalizable and that the self-consistent scheme
follows Baym''s -derivable concept. The scheme generates both, the
renormalized self-consistent equations of motion and the closed equations for
the infinite set of counter terms. At the same time the corresponding
2PI-generating functional and the thermodynamical potential can be
renormalized, in consistency with the equations of motion. This guarantees the
standard -derivable properties like thermodynamic consistency and exact
conservation laws also for the renormalized approximation schemes to hold. The
proof uses the techniques of BPHZ-renormalization to cope with the explicit and
the hidden overlapping vacuum divergences.Comment: 22 Pages 1 figure, uses RevTeX4. The Revision concerns the correction
of some minor typos, a clarification concerning the real-time contour
structure of renormalization parts and some comments concerning symmetries in
the conclusions and outloo
Damping Rates and Mean Free Paths of Soft Fermion Collective Excitations in a Hot Fermion-Gauge-Scalar Theory
We study the transport coefficients, damping rates and mean free paths of
soft fermion collective excitations in a hot fermion-gauge-scalar plasma with
the goal of understanding the main physical mechanisms that determine transport
of chirality in scenarios of non-local electroweak baryogenesis. The focus is
on identifying the different transport coefficients for the different branches
of soft collective excitations of the fermion spectrum. These branches
correspond to collective excitations with opposite ratios of chirality to
helicity and different dispersion relations. By combining results from the hard
thermal loop (HTL) resummation program with a novel mechanism of fermion
damping through heavy scalar decay, we obtain a robust description of the
different damping rates and mean free paths for the soft collective excitations
to leading order in HTL and lowest order in the Yukawa coupling. The space-time
evolution of wave packets of collective excitations unambiguously reveals the
respective mean free paths. We find that whereas both the gauge and scalar
contribution to the damping rates are different for the different branches, the
difference of mean free paths for both branches is mainly determined by the
decay of the heavy scalar into a hard fermion and a soft collective excitation.
We argue that these mechanisms are robust and are therefore relevant for
non-local scenarios of baryogenesis either in the Standard Model or extensions
thereof.Comment: REVTeX, 19 pages, 4 eps figures, published versio
Evolution of Inhomogeneous Condensates after Phase Transitions
Using the O(4) linear model, we address the topic of non-equilibrium
relaxation of an inhomogeneous initial configuration due to quantum and thermal
fluctuations. The space-time evolution of an inhomogeneous fluctuation of the
condensate in the isoscalar channel decaying via the emission of pions in the
medium is studied within the context of disoriented chiral condensates. We use
out of equilibrium closed time path methods in field theory combined with the
amplitude expansion. We give explicit expressions for the asymptotic space-time
evolution of an initial inhomogeneous configuration including the contribution
of thresholds at zero and non-zero temperature. At non-zero temperature we find
new relaxational processes due to thermal cuts that have no counterpart in the
homogeneous case. Within the one-loop approximation, we find that the space
time evolution of such inhomogeneous configuration out of equilibrium is
effectively described in terms of a rapidity dependent temperature
as well as a rapidity dependent decay rate
. This rate is to be interpreted as the
production minus absorption rate of pions in the medium and approaches the zero
temperature value at large rapidities. An initial configuration localized on a
bounded region spreads and decays in spherical waves with slower relaxational
dynamics at large rapidity.Comment: 25 pages Revtex 3.0, two figures available upon reques
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