187 research outputs found
Schwinger-Keldysh Propagators from AdS/CFT Correspondence
We demonstrate how to compute real-time Green's functions for a class of
finite temperature field theories from their AdS gravity duals. In particular,
we reproduce the two-by-two Schwinger-Keldysh matrix propagator from a gravity
calculation. Our methods should work also for computing higher point Lorentzian
signature correlators. We elucidate the boundary condition subtleties which
hampered previous efforts to build a Lorentzian-signature AdS/CFT
correspondence. For two-point correlators, our construction is automatically
equivalent to the previously formulated prescription for the retarded
propagator.Comment: 16 pages, 1 figure, references added; to appear in JHE
On time-dependent AdS/CFT
We clarify aspects of the holographic AdS/CFT correspondence that are typical
of Lorentzian signature, to lay the foundation for a treatment of
time-dependent gravity and conformal field theory phenomena. We provide a
derivation of bulk-to-boundary propagators associated to advanced, retarded and
Feynman bulk propagators, and provide a better understanding of the boundary
conditions satisfied by the bulk fields at the horizon. We interpret the
subleading behavior of the wavefunctions in terms of specific vacuum
expectation values, and compute two-point functions in our framework. We
connect our bulk methods to the closed time path formalism in the boundary
field theory.Comment: 19 pages, v2: added reference, JHEP versio
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
Quantum fields in disequilibrium: neutral scalar bosons with long-range, inhomogeneous perturbations
Using Schwinger's quantum action principle, dispersion relations are obtained
for neutral scalar mesons interacting with bi-local sources. These relations
are used as the basis of a method for representing the effect of interactions
in the Gaussian approximation to field theory, and it is argued that a marked
inhomogeneity, in space-time dependence of the sources, forces a discrete
spectrum on the field. The development of such a system is characterized by
features commonly associated with chaos and self-organization (localization by
domain or cell formation). The Green functions play the role of an iterative
map in phase space. Stable systems reside at the fixed points of the map. The
present work can be applied to self-interacting theories by choosing suitable
properties for the sources. Rapid transport leads to a second order phase
transition and anomalous dispersion. Finally, it is shown that there is a
compact representation of the non-equilibrium dynamics in terms of generalized
chemical potentials, or equivalently as a pseudo-gauge theory, with an
imaginary charge. This analogy shows, more clearly, how dissipation and entropy
production are related to the source picture and transform a flip-flop like
behaviour between two reservoirs into the Landau problem in a constant
`magnetic field'. A summary of conventions and formalism is provided as a basis
for future work.Comment: 23 pages revte
A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions
A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for
the n-point Green functions and the amputated 1PI vertex functions at finite
temperature is derived in the framework of the Closed Time Path formalism. We
verify that this generalized FDT coincides with known results for n=2 and 3.
New explicit relations among the 4-point nonlinear response and correlation
(fluctuation) functions are presented.Comment: 34 pages, Revte
Schwinger-Dyson approach to non-equilibrium classical field theory
In this paper we discuss a Schwinger-Dyson [SD] approach for determining the
time evolution of the unequal time correlation functions of a non-equilibrium
classical field theory, where the classical system is described by an initial
density matrix at time . We focus on field theory in 1+1
space time dimensions where we can perform exact numerical simulations by
sampling an ensemble of initial conditions specified by the initial density
matrix. We discuss two approaches. The first, the bare vertex approximation
[BVA], is based on ignoring vertex corrections to the SD equations in the
auxiliary field formalism relevant for 1/N expansions. The second approximation
is a related approximation made to the SD equations of the original formulation
in terms of alone. We compare these SD approximations as well as a
Hartree approximation with exact numerical simulations. We find that both
approximations based on the SD equations yield good agreement with exact
numerical simulations and cure the late time oscillation problem of the Hartree
approximation. We also discuss the relationship between the quantum and
classical SD equations.Comment: 36 pages, 5 figure
Nonequilibrium Evolution of Correlation Functions: A Canonical Approach
We study nonequilibrium evolution in a self-interacting quantum field theory
invariant under space translation only by using a canonical approach based on
the recently developed Liouville-von Neumann formalism. The method is first
used to obtain the correlation functions both in and beyond the Hartree
approximation, for the quantum mechanical analog of the model. The
technique involves representing the Hamiltonian in a Fock basis of annihilation
and creation operators. By separating it into a solvable Gaussian part
involving quadratic terms and a perturbation of quartic terms, it is possible
to find the improved vacuum state to any desired order. The correlation
functions for the field theory are then investigated in the Hartree
approximation and those beyond the Hartree approximation are obtained by
finding the improved vacuum state corrected up to . These
correlation functions take into account next-to-leading and
next-to-next-to-leading order effects in the coupling constant. We also use the
Heisenberg formalism to obtain the time evolution equations for the equal-time,
connected correlation functions beyond the leading order. These equations are
derived by including the connected 4-point functions in the hierarchy. The
resulting coupled set of equations form a part of infinite hierarchy of coupled
equations relating the various connected n-point functions. The connection with
other approaches based on the path integral formalism is established and the
physical implications of the set of equations are discussed with particular
emphasis on thermalization.Comment: Revtex, 32 pages; substantial new material dealing with
non-equilibrium evolution beyond Hartree approx. based on the LvN formalism,
has been adde
The Trouble with de Sitter Space
In this paper we assume the de Sitter Space version of Black Hole
Complementarity which states that a single causal patch of de Sitter space is
described as an isolated finite temperature cavity bounded by a horizon which
allows no loss of information. We discuss the how the symmetries of de Sitter
space should be implemented. Then we prove a no go theorem for implementing the
symmetries if the entropy is finite. Thus we must either give up the finiteness
of the de Sitter entropy or the exact symmetry of the classical space. Each has
interesting implications for the very long time behavior. We argue that the
lifetime of a de Sitter phase can not exceed the Poincare recurrence time. This
is supported by recent results of Kachru, Kallosh, Linde and Trivedi.Comment: 15 pages, 1 figure. v2: added fifth section with comments on long
time stability of de Sitter space, in which we argue that the lifetime can
not exceed the Poincare recurrence time. v3: corrected a minor error in the
appendi
Correlation Entropy of an Interacting Quantum Field and H-theorem for the O(N) Model
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy
(of the nth order) for an interacting quantum field, obtained by `slaving'
(truncation with causal factorization) of the higher (n+1 th) order correlation
functions in the Schwinger-Dyson system of equations. This renders an otherwise
closed system effectively open where dissipation arises. The concept of
correlation entropy is useful for addressing issues related to thermalization.
As a small yet important step in that direction we prove an H-theorem for the
correlation entropy of a quantum mechanical O(N) model with a Closed Time Path
Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order
large N approximation. This model may be regarded as a field theory in
space dimensions.Comment: 22 page
Infrared Behaviour of The Gluon Propagator in Non-Equilibrium Situations
The infrared behaviour of the medium modified gluon propagator in
non-equilibrium situations is studied in the covariant gauge using the
Schwinger-Keldysh closed-time path formalism. It is shown that the magnetic
screening mass is non-zero at the one loop level whenever the initial gluon
distribution function is non isotropic with the assumption that the
distribution function of the gluon is not divergent at zero transverse
momentum. For isotropic gluon distribution functions, such as those describing
local equilibrium, the magnetic mass at one loop level is zero which is
consistent with finite temperature field theory results. Assuming that a
reasonable initial gluon distribution function can be obtained from a
perturbative QCD calculation of minijets, we determine these out of equilibrium
values for the initial magnetic and Debye screening masses at energy densities
appropriate to RHIC and LHC. We also compare the magnetic masses obtained here
with those obtained using finite temperature lattice QCD methods at similar
temperatures at RHIC and LHC.Comment: 21 pages latex, 4 figures, final version to be published in Phys.
Rev.
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