63 research outputs found
Historical Hamiltonian Dynamics: symplectic and covariant
This paper presents a " historical " formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field theories on space-time. It is based on the notion of (Hamiltonian) histories, which are sections of the (extended) phase space bundle. It is developed in the space of sections, in contradistinction with the usual formalism which works in the bundle manifold. In field theories, the formalism remains covariant and does not require a spitting of space-time. It considers space-time exactly in the same manner than time in usual dynamics, both being particular cases of the evolution domain. It applies without modification when the histories (the fields) are forms rather than scalar functions, like in electromagnetism or in tetrad general relativity. We develop a differential calculus in the infinite dimensional space of histories. It admits a (generalized) symplectic form which does not break the covariance. We develop a covariant symplectic formalism, with generalizations of usual notions like current conservation, Hamiltonian vector-fields, evolution vector-field, brackets, ... The usual multisymplectic approach derives form it, as well as the symplectic form introduced by Crnkovic and Witten in the space of solutions
A symplectic approach to gravitational instability
We present a global approach of non-dissipative physics. Based on symplectic
mechanics this technique allows us to obtain the solution of a very large class
of problems in terms of a Taylor expand. We apply this method to the problem of
gravitational instability and we obtain a general expression of the
gravitational potential, solution of the Vlasov- Poisson gravitational
potential, solution of the Vlasov-Poisson system, as a function of time in the
context of Newtonian dust cosmology.Comment: uuencoded compressed postscript file containing 14 pages, accepted
for publication in Ap
Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval
We present a quantization scheme of an arbitrary measure space based on
overcomplete families of states and generalizing the Klauder and the
Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient
tool for quantizing physical systems for which more traditional methods like
geometric quantization are uneasy to implement. The procedure is illustrated by
(mostly two-dimensional) elementary examples in which the measure space is a
-element set and the unit interval. Spaces of states for the -element set
and the unit interval are the 2-dimensional euclidean and hermitian
\C^2 planes
Measuring Statistical isotropy of the CMB anisotropy
The statistical expectation values of the temperature fluctuations of cosmic
microwave background (CMB) are assumed to be preserved under rotations of the
sky. This assumption of {\em statistical isotropy} (SI) of the CMB anisotropy
should be observationally verified since detection of violation of SI could
have profound implications for cosmology. We propose a set of measures,
() for detecting violation of statistical
isotropy in an observed CMB anisotropy sky map indicated by non zero
. We define an estimator for the spectrum and
analytically compute its cosmic bias and cosmic variance. The results match
those obtained by measuring using simulated sky maps. Non-zero
(bias corrected) larger than the SI cosmic variance will imply
violation of SI. The SI measure proposed in this paper is an appropriate
statistics to investigate preliminary indication of SI violation in the
recently released WMAP data.Comment: 9 pages, 1 figure, Style file changed, figure enhanced and references
update
About the Malmquist bias in the determination of H0 and of distances of galaxies
We provide the mathematical framework which elucidates the way of using a
Tully-Fisher (TF) like relation in the determination of the Hubble constant
, as well as for distances of galaxies. The methods related to the
so-called Direct and Inverse TF Relations (herein DTF and ITF) are interpreted
as maximum likelihood statistics. We show that, as long as the same model is
used for the calibration of the TF relation and for the determination of ,
we obtain a coherent Hubble's constant. The choice of the model is motivated by
reasons of robustness of statistics, it depends on selection effects in
observation which are present in the sample. The difference on the distance
estimates when using either the ITF or the DTF model is only due to random
fluctuations. It is interesting to point out that the DTF estimate does not
depend on the luminosity distribution of sources. Both statistics show a
correction for a bias, inadequately believed to be of Malmquist type. The
repercussion of measurement errors, and additional selection effects are also
analyzedComment: 37 pages,cpt-93/p.2808,latex A&A,4fig available on cpt.univ-mrs.fr
directory ftp/pub/preprints/93/cosmology/93-P.280
Pure Luminosity Evolution Hypothesis for QSOs: From Luminosity Functions to Synthetic Catalogues
This paper describes the simulation of realistic Monte-Carlo extragalactic
catalogues, aimed at comparing the behaviour of cosmological tests versus input
parameters. QSO catalogues are built on a Luminosity Function derived from data
through suitable computation of individual maximum volumes in complete (but
magnitude- and redshift-limited) samples requiring neither of redshift nor of
apparent magnitude histogram. The values of the evolution parameter are derived
for various cosmologies, corresponding to =1/2 in the sample of 400
Ultra-Violet Excess (UVX) QSOs (Boyle et al 1990). The various luminosity
functions are compared, both for the whole sample and in redshift bins. An
evolution characteristic time is defined and computed, depending strongly on
the cosmology, but practically constant when expressed in terms of the age of
the Universe. Algorithms are given for producing unbiased or biased catalogues
based on the null hypothesis that the objects are uniformly distributed in
volume but suffer Pure Luminosity Evolution.Comment: uuencode compressed tar file of Latex and macros files. Tar
compressed poscript files of the papers and figures are also available by
anonymous ftp at ftp://summer.obs-mip.fr/pub/OUTGOING/paper2 or upon request
at [email protected]
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