76 research outputs found
Gell-Mann and Low formula for degenerate unperturbed states
The Gell-Mann and Low switching allows to transform eigenstates of an
unperturbed Hamiltonian into eigenstates of the modified Hamiltonian . This switching can be performed when the initial eigenstate is not
degenerate, under some gap conditions with the remainder of the spectrum. We
show here how to extend this approach to the case when the ground state of the
unperturbed Hamiltonian is degenerate. More precisely, we prove that the
switching procedure can still be performed when the initial states are
eigenstates of the finite rank self-adjoint operator \cP_0 V \cP_0, where
\cP_0 is the projection onto a degenerate eigenspace of
Hot String Soup
Above the Hagedorn energy density closed fundamental strings form a long
string phase. The dynamics of weakly interacting long strings is described by a
simple Boltzmann equation which can be solved explicitly for equilibrium
distributions. The average total number of long strings grows logarithmically
with total energy in the microcanonical ensemble. This is consistent with
calculations of the free single string density of states provided the
thermodynamic limit is carefully defined. If the theory contains open strings
the long string phase is suppressed.Comment: 13 pages, no figures, uses LaTex, some errors in equations have been
corrected, NSF-ITP-94-83, UCSBTH-94-3
Information measures and classicality in quantum mechanics
We study information measures in quantu mechanics, with particular emphasis
on providing a quantification of the notions of classicality and
predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a
precise criterion for phase space classicality and argue that in view of this
a) I provides a measure of the degree of deviation from classicality for closed
system b) I - S (S the von Neumann entropy) plays the same role in open systems
We examine particular examples in non-relativistic quantum mechanics. Finally,
(this being one of our main motivations) we comment on field classicalisation
on early universe cosmology.Comment: 35 pages, LATE
Decoupling of Degenerate Positive-norm States in Witten's String Field Theory
We show that the degenerate positive-norm physical propagating fields of the
open bosonic string can be gauged to the higher rank fields at the same mass
level. As a result, their scattering amplitudes can be determined from those of
the higher spin fields. This phenomenon arises from the existence of two types
of zero-norm states with the same Young representations as those of the
degenerate positive-norm states in the old covariant first quantized (OCFQ)
spectrum. This is demonstrated by using the lowest order gauge transformation
of Witten's string field theory (WSFT) up to the fourth massive level
(spin-five), and is found to be consistent with conformal field theory
calculation based on the first quantized generalized sigma-model approach. In
particular, on-shell conditions of zero-norm states in OCFQ stringy gauge
transformation are found to correspond, in a one-to-one manner, to the
background ghost fields in off-shell gauge transformation of WSFT. The
implication of decoupling of scalar modes on Sen's conjectures was also briefly
discussed.Comment: 18 pages, use Latex with revtex
The QCD Phase Structure at High Baryon Density
We consider the possibility that color deconfinement and chiral symmetry
restoration do not coincide in dense baryonic matter at low temperature. As a
consequence, a state of massive "constituent" quarks would exist as an
intermediate phase between confined nuclear matter and the plasma of deconfined
massless quarks and gluons. We discuss the properties of this state and its
relation to the recently proposed quarkyonic matter.Comment: 17 pages, 9 figure
Could thermal fluctuations seed cosmic structure?
We examine the possibility that thermal, rather than quantum, fluctuations
are responsible for seeding the structure of our universe. We find that while
the thermalization condition leads to nearly Gaussian statistics, a
Harrisson-Zeldovich spectrum for the primordial fluctuations can only be
achieved in very special circumstances. These depend on whether the universe
gets hotter or colder in time, while the modes are leaving the horizon. In the
latter case we find a no-go theorem which can only be avoided if the
fundamental degrees of freedom are not particle-like, such as in string gases
near the Hagedorn phase transition. The former case is less forbidding, and we
suggest two potentially successful ``warming universe'' scenarios. One makes
use of the Phoenix universe, the other of ``phantom'' matter.Comment: minor corrections made, references added, matches the version
accepted to PR
Thermodynamic behavior of IIA string theory on a pp-wave
We obtain the thermal one loop free energy and the Hagedorn temperature of
IIA superstring theory on the pp-wave geometry which comes from the circle
compactification of the maximally supersymmetric eleven dimensional one. We use
both operator and path integral methods and find the complete agreement between
them in the free energy expression. In particular, the free energy in the limit is shown to be identical with that of IIB string theory on
maximally supersymmetric pp-wave, which indicates the universal thermal
behavior of strings in the large class of pp-wave backgrounds. We show that the
zero point energy and the modular properties of the free energy are naturally
incorporated into the path integral formalism.Comment: 25 pages, Latex, JHEP style, v4: revised for clarity without change
in main contents, version to appear in JHE
Thermal history of the string universe
Thermal history of the string universe based on the Brandenberger and Vafa's
scenario is examined. The analysis thereby provides a theoretical foundation of
the string universe scenario. Especially the picture of the initial oscillating
phase is shown to be natural from the thermodynamical point of view. A new tool
is employed to evaluate the multi state density of the string gas. This
analysis points out that the well-known functional form of the multi state
density is not applicable for the important region , and derives a
correct form of it.Comment: 39 pages, no figures, use revtex.sty, aps.sty, aps10.sty &
preprint.st
Aspects of String-Gas Cosmology at Finite Temperature
We study string-gas cosmology in dilaton gravity, inspired by the fact that
it naturally arises in a string theory context. Our main interest is the
thermodynamical treatment of the string-gas and the resulting implications for
the cosmology. Within an adiabatic approximation, thermodynamical equilibrium
and a small, toroidal universe as initial conditions, we numerically solve the
corresponding equations of motions in two different regimes describing the
string-gas thermodynamics: (i) the Hagedorn regime, with a single scale factor,
and (ii) an almost-radiation dominated regime, which includes the leading
corrections due to the lightest Kaluza Klein and winding modes, with two scale
factors. The scale factor in the Hagedorn regime exhibits very slow time
evolution with nearly constant energy and negligible pressure. By contrast, in
case (ii) we find interesting cosmological solutions where the large dimensions
continue to expand and the small ones are kept undetectably small.Comment: 21 pages, 5 eps figure
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