48 research outputs found
Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical commutation rule Dirac missed
Dirac's identification of the quantum analog of the Poisson bracket with the
commutator is reviewed, as is the threat of self-inconsistent overdetermination
of the quantization of classical dynamical variables which drove him to
restrict the assumption of correspondence between quantum and classical Poisson
brackets to embrace only the Cartesian components of the phase space vector.
Dirac's canonical commutation rule fails to determine the order of noncommuting
factors within quantized classical dynamical variables, but does imply the
quantum/classical correspondence of Poisson brackets between any linear
function of phase space and the sum of an arbitrary function of only
configuration space with one of only momentum space. Since every linear
function of phase space is itself such a sum, it is worth checking whether the
assumption of quantum/classical correspondence of Poisson brackets for all such
sums is still self-consistent. Not only is that so, but this slightly stronger
canonical commutation rule also unambiguously determines the order of
noncommuting factors within quantized dynamical variables in accord with the
1925 Born-Jordan quantization surmise, thus replicating the results of the
Hamiltonian path integral, a fact first realized by E. H. Kerner. Born-Jordan
quantization validates the generalized Ehrenfest theorem, but has no inverse,
which disallows the disturbing features of the poorly physically motivated
invertible Weyl quantization, i.e., its unique deterministic classical "shadow
world" which can manifest negative densities in phase space.Comment: 12 pages, Final publication in Foundations of Physics; available
online at http://www.springerlink.com/content/k827666834140322
Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations
Partition functions for non-interacting particles are known to be symmetric
functions. It is shown that powerful group-theoretical techniques can be used
not only to derive these relationships, but also to significantly simplify
calculation of the partition functions for particles that carry internal
quantum numbers. The partition function is shown to be a sum of one or more
group characters. The utility of character expansions in calculating the
partition functions is explored. Several examples are given to illustrate these
techniques.Comment: 16 pages of RevTe
A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey
We provide exact solutions to the cosmological matter perturbation equation
in a homogeneous FLRW universe with a vacuum energy that can be parametrized by
a constant equation of state parameter and a very accurate approximation
for the Ansatz . We compute the growth index \gamma=\log
f(a)/\log\Om_m(a), and its redshift dependence, using the exact and
approximate solutions in terms of Legendre polynomials and show that it can be
parametrized as in most cases. We then
compare four different types of dark energy (DE) models: CDM, DGP,
and a LTB-large-void model, which have very different behaviors at
z\gsim1. This allows us to study the possibility to differentiate between
different DE alternatives using wide and deep surveys like Euclid, which will
measure both photometric and spectroscopic redshifts for several hundreds of
millions of galaxies up to redshift . We do a Fisher matrix analysis
for the prospects of differentiating among the different DE models in terms of
the growth index, taken as a given function of redshift or with a principal
component analysis, with a value for each redshift bin for a Euclid-like
survey. We use as observables the complete and marginalized power spectrum of
galaxies and the Weak Lensing (WL) power spectrum. We find that, using
, one can reach (2%, 5%) errors in , and (4%, 12%) errors in
, while using WL we get errors at least twice as large.
These estimates allow us to differentiate easily between DGP, models and
CDM, while it would be more difficult to distinguish the latter from a
variable equation of state parameter or LTB models using only the growth
index.}Comment: 29 pages, 7 figures, 6 table
The Formation of Cosmic Structures in a Light Gravitino Dominated Universe
We analyse the formation of cosmic structures in models where the dark matter
is dominated by light gravitinos with mass of eV -- 1 keV, as predicted
by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the
number of degrees of freedom at the gravitinos decoupling (), we compute
the transfer function for matter fluctuations and show that gravitinos behave
like warm dark matter (WDM) with free-streaming scale comparable to the galaxy
mass scale. We consider different low-density variants of the WDM model, both
with and without cosmological constant, and compare the predictions on the
abundances of neutral hydrogen within high-redshift damped Ly-- systems
and on the number density of local galaxy clusters with the corresponding
observational constraints. We find that none of the models satisfies both
constraints at the same time, unless a rather small value (\mincir
0.4) and a rather large Hubble parameter (\magcir 0.9) is assumed.
Furthermore, in a model with warm + hot dark matter, with hot component
provided by massive neutrinos, the strong suppression of fluctuation on scales
of \sim 1\hm precludes the formation of high-redshift objects, when the
low-- cluster abundance is required. We conclude that all different variants
of a light gravitino DM dominated model show strong difficulties for what
concerns cosmic structure formation.
This gives a severe cosmological constraint on the gauge-mediated SUSY
breaking scheme.Comment: 28 pages,Latex, submitted for publication to Phys.Rev.
Stellar population synthesis at the resolution of 2003
We present a new model for computing the spectral evolution of stellar
populations at ages between 100,000 yr and 20 Gyr at a resolution of 3 A across
the whole wavelength range from 3200 to 9500 A for a wide range of
metallicities. These predictions are based on a newly available library of
observed stellar spectra. We also compute the spectral evolution across a
larger wavelength range, from 91 A to 160 micron, at lower resolution. The
model incorporates recent progress in stellar evolution theory and an
observationally motivated prescription for thermally-pulsing stars on the
asymptotic giant branch. The latter is supported by observations of surface
brightness fluctuations in nearby stellar populations. We show that this model
reproduces well the observed optical and near-infrared colour-magnitude
diagrams of Galactic star clusters of various ages and metallicities.
Stochastic fluctuations in the numbers of stars in different evolutionary
phases can account for the full range of observed integrated colours of star
clusters in the Magellanic Clouds. The model reproduces in detail typical
galaxy spectra from the Early Data Release (EDR) of the Sloan Digital Sky
Survey (SDSS). We exemplify how this type of spectral fit can constrain
physical parameters such as the star formation history, metallicity and dust
content of galaxies. Our model is the first to enable accurate studies of
absorption-line strengths in galaxies containing stars over the full range of
ages. Using the highest-quality spectra of the SDSS EDR, we show that this
model can reproduce simultaneously the observed strengths of those Lick indices
that do not depend strongly on element abundance ratios [abridged].Comment: 35 pages, 22 figures, to appear in MNRAS; version with full
resolution figures available at http://www.iap.fr/~charlot/bc2003/pape
Has the Rate of CD4 Cell Count Decline before Initiation of Antiretroviral Therapy Changed over the Course of the Dutch HIV Epidemic among MSM?
Introduction:Studies suggest that the HIV-1 epidemic in the Netherlands may have become more virulent, leading to faster disease progression if untreated. Analysis of CD4 cell count decline before antiretroviral therapy (ART) initiation, a surrogate marker for disease progression, may be hampered by informative censoring as ART initiation is more likely with a steeper CD4 cell count decline.Methods:Development of CD4 cell count from 9 to 48 months after seroconversion was analyzed using a mixed-effects model and 2 models that jointly modeled CD4 cell counts and time to censoring event (start ART
Non-AIDS defining cancers in the D:A:D Study-time trends and predictors of survival : a cohort study
BACKGROUND:Non-AIDS defining cancers (NADC) are an important cause of morbidity and mortality in HIV-positive individuals. Using data from a large international cohort of HIV-positive individuals, we described the incidence of NADC from 2004-2010, and described subsequent mortality and predictors of these.METHODS:Individuals were followed from 1st January 2004/enrolment in study, until the earliest of a new NADC, 1st February 2010, death or six months after the patient's last visit. Incidence rates were estimated for each year of follow-up, overall and stratified by gender, age and mode of HIV acquisition. Cumulative risk of mortality following NADC diagnosis was summarised using Kaplan-Meier methods, with follow-up for these analyses from the date of NADC diagnosis until the patient's death, 1st February 2010 or 6 months after the patient's last visit. Factors associated with mortality following NADC diagnosis were identified using multivariable Cox proportional hazards regression.RESULTS:Over 176,775 person-years (PY), 880 (2.1%) patients developed a new NADC (incidence: 4.98/1000PY [95% confidence interval 4.65, 5.31]). Over a third of these patients (327, 37.2%) had died by 1st February 2010. Time trends for lung cancer, anal cancer and Hodgkin's lymphoma were broadly consistent. Kaplan-Meier cumulative mortality estimates at 1, 3 and 5 years after NADC diagnosis were 28.2% [95% CI 25.1-31.2], 42.0% [38.2-45.8] and 47.3% [42.4-52.2], respectively. Significant predictors of poorer survival after diagnosis of NADC were lung cancer (compared to other cancer types), male gender, non-white ethnicity, and smoking status. Later year of diagnosis and higher CD4 count at NADC diagnosis were associated with improved survival. The incidence of NADC remained stable over the period 2004-2010 in this large observational cohort.CONCLUSIONS:The prognosis after diagnosis of NADC, in particular lung cancer and disseminated cancer, is poor but has improved somewhat over time. Modifiable risk factors, such as smoking and low CD4 counts, were associated with mortality following a diagnosis of NADC