1,613 research outputs found
Large N Quantum Time Evolution Beyond Leading Order
For quantum theories with a classical limit (which includes the large N
limits of typical field theories), we derive a hierarchy of evolution equations
for equal time correlators which systematically incorporate corrections to the
limiting classical evolution. Explicit expressions are given for
next-to-leading order, and next-to-next-to-leading order time evolution. The
large N limit of N-component vector models, and the usual semiclassical limit
of point particle quantum mechanics are used as concrete examples. Our
formulation directly exploits the appropriate group structure which underlies
the construction of suitable coherent states and generates the classical phase
space. We discuss the growth of truncation error with time, and argue that
truncations of the large-N evolution equations are generically expected to be
useful only for times short compared to a ``decoherence'' time which scales
like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float
Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
We prove an equivalence, in the large N limit, between certain U(N) gauge
theories containing adjoint representation matter fields and their orbifold
projections. Lattice regularization is used to provide a non-perturbative
definition of these theories; our proof applies in the strong coupling, large
mass phase of the theories. Equivalence is demonstrated by constructing and
comparing the loop equations for a parent theory and its orbifold projections.
Loop equations for both expectation values of single-trace observables, and for
connected correlators of such observables, are considered; hence the
demonstrated non-perturbative equivalence applies to the large N limits of both
string tensions and particle spectra.Comment: 40 pages, JHEP styl
Towards a Realistic Equation of State of Strongly Interacting Matter
We consider a relativistic strongly interacting Bose gas. The interaction is
manifested in the off-shellness of the equilibrium distribution. The equation
of state that we obtain for such a gas has the properties of a realistic
equation of state of strongly interacting matter, i.e., at low temperature it
agrees with the one suggested by Shuryak for hadronic matter, while at high
temperature it represents the equation of state of an ideal ultrarelativistic
Stefan-Boltzmann gas, implying a phase transition to an effectively weakly
interacting phase.Comment: LaTeX, figures not include
An improved time-dependent Hartree-Fock approach for scalar \phi^4 QFT
The model in a finite volume is studied within a
non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of
equilibrium, with particular attention to the structure of the ground state and
of certain dynamical features in the broken symmetry phase. The mean-field
coupled time-dependent Schroedinger equations for the modes of the scalar field
are derived and the suitable procedure to renormalize them is outlined. A
further controlled gaussian approximation of our tdHF approach is used in order
to study the dynamical evolution of the system from non-equilibrium initial
conditions characterized by a uniform condensate. We find that, during the slow
rolling down, the long-wavelength quantum fluctuations do not grow to a
macroscopic size but do scale with the linear size of the system, in accordance
with similar results valid for the large approximation of the O(N) model.
This behavior undermines in a precise way the gaussian approximation within our
tdHF approach, which therefore appears as a viable mean to correct an unlikely
feature of the standard HF factorization scheme, such as the so-called
``stopping at the spinodal line'' of the quantum fluctuations. We also study
the dynamics of the system in infinite volume with particular attention to the
asymptotic evolution in the broken symmetry phase. We are able to show that the
fixed points of the evolution cover at most the classically metastable part of
the static effective potential.Comment: Accepted for publication on Phys. Rev.
Some New/Old Approaches to QCD
This is a talk delivered at the Meeting on Integrable Quantum Field Theories,
Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent
attempts to revive two old ideas regarding an analytic approach to QCD-the
development of a string representation of the theory and the large N limit of
QCD.Comment: 20 page
Quark-Gluon Plasma - New Frontiers
As implied by organizers, this talk is not a conference summary but rather an
outline of progress/challenges/``frontiers'' of the theory. Some fundamental
questions addressed are:
Why is sQGP such a good liquid? Do we understand (de)confinement and what do
we know about ``magnetic'' objects creating it? Can we understand the AdS/CFT
predictions, from the gauge theory side? Can they be tested experimentally? Can
AdS/CFT duality help us understand rapid equilibration/entropy production? Can
we work out a complete dynamical ``gravity dual'' to heavy ion collisions?Comment: final talk at Quark Matter 2008, Jaipur, India, Feb.200
Electroweak bubbles and sphalerons
We consider non-perturbative solutions of the Weinberg-Salam model at finite
temperature. We employ an effective temperature-dependent potential yielding a
first order phase transition. In the region of the phase transition, there
exist two kinds of static, spherically symmetric solutions: sphalerons and
bubbles. We analyze these solutions as functions of temperature. We consider
the most general spherically symmetric fluctuations about the two solutions and
construct the discrete modes in the region of the phase transition. Sphalerons
and bubbles both possess a single unstable mode. We present simple
approximation formulae for these levels.Comment: 14 pages, plain tex, 9 figures appended as postscript files at the
end of the paper. THU-93/0
Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
We present a study of the free energy of parameterized Polyakov loops P in
SU(2) and SU(3) lattice gauge theory as a function of the parameters that
characterize P. We explore temperatures below and above the deconfinement
transition, and for our highest temperatures T > 5 T_c we compare the free
energy to perturbative results.Comment: Minor changes. Final version to appear in JHE
Potts Flux Tube Model at Nonzero Chemical Potential
We model the deconfinement phase transition in quantum chromodynamics at
nonzero baryon number density and large quark mass by extending the flux tube
model (three-state, three-dimensional Potts model) to nonzero chemical
potential. In a direct numerical simulation we confirm mean-field-theory
predictions that the deconfinement transition does not occur in a baryon-rich
environment.Comment: 14 pp RevTeX, 10 Postscript figures, submitted to Phys. Rev D.
(Corrected some typographical errors.
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