29,124 research outputs found
Dynamics of Totally Constrained Systems II. Quantum Theory
In this paper a new formulation of quantum dynamics of totally constrained
systems is developed, in which physical quantities representing time are
included as observables. In this formulation the hamiltonian constraints are
imposed on a relative probability amplitude functional which determines
the relative probability for each state to be observed, instead of on the state
vectors as in the conventional Dirac quantization. This leads to a foliation of
the state space by linear manifolds on each of which is constant, and
dynamics is described as linear mappings among acausal subspaces which are
transversal to these linear manifolds. This is a quantum analogue of the
classical statistical dynamics of totally constrained systems developed in the
previous paper. It is shown that if the von Neumann algebra \C generated by
the constant of motion is of type I, can be consistently normalizable on
the acausal subspaces on which a factor subalgebra of \C is represented
irreducibly, and the mappings among these acausal subspaces are conformal. How
the formulation works is illustrated by simple totally constrained systems with
a single constraint such as the parametrized quantum mechanics, a relativistic
free particle in Minkowski and curved spacetimes, and a simple minisuperspace
model. It is pointed out that the inner product of the relative probability
amplitudes induced from the original Hilbert space picks up a special
decomposition of the wave functions to the positive and the negative frequency
modes.Comment: 57 pages, some unexpected control codes in the original file, which
may cause errors for some LaTeX compilers, were remove
Dynamics of Totally Constrained Systems I. Classical Theory
This is the first of a series of papers in which a new formulation of quantum
theory is developed for totally constrained systems, that is, canonical systems
in which the hamiltonian is written as a linear combination of constraints
with arbitrary coefficients. The main purpose of the present paper
is to make clear that classical dynamics of a totally constrained system is
nothing but the foliation of the constraint submanifold in phase space by the
involutive system of infinitesimal canonical transformations
generated by the constraint functions. From this point of view it is shown that
statistical dynamics for an ensemble of a totally constrained system can be
formulated in terms of a relative distribution function without gauge fixing or
reduction. There the key role is played by the fact that the canonical measure
in phase space and the vector fields induce natural conservative
measures on acausal submanifolds, which are submanifolds transversal to the
dynamical foliation. Further it is shown that the structure coefficients
defined by should weakly commute with ,
, in order that the
description in terms of the relative distribution function is consistent. The
overall picture on the classical dynamics given in this paper provides the
basic motivation for the quantum formulation developed in the subsequent
papers.Comment: 31 pages, LaTeX fil
Behavior of Cosmological Perturbations in the Brane-World Mode
In this paper we present a gauge-invariant formalism for perturbations of the
brane-world model developed by the author, A. Ishibashi and O. Seto recently,
and analyze the behavior of cosmological perturbations in a spatially flat
expanding universe realized as a boundary 3-brane in AdS in terms of this
formalism. For simplicity we restrict arguments to scalar perturbations. We
show that the behavior of cosmological perturbations on superhorizon scales in
the brane-world model is the same as that in the standard no-extradimension
model, irrespective of the initial condition for bulk perturbations, in the
late stage when the cosmic expansion rate is smaller than the inverse of
the bulk curvature scale . Further, we give rough estimates which
indicate that in the early universe when is much larger than ,
perturbations in these two models behave quite differently, and the
conservation of the Bardeen parameter does not hold for superhorizon
perturbations in the brane-world model.Comment: 4 pages in the revtex style. A talk in the conference CAPP2000 to be
published in the proceeding
The Mass Assembly History of Galaxies and Clusters of Galaxies
We discuss the mass assembly history both on cluster and galaxy scales and
their impact on galaxy evolution. On cluster scale, we introduce our on-going
PISCES project on Subaru, which plans to target ~15 clusters at 0.4<z<1.3 using
the unique wide-field (30') optical camera Suprime-Cam and the spectrograph
both in optical (FOCAS, 6') and near-infrared (FMOS, 30'). The main objectives
of this project are twofold: (1) Mapping out the large scale structures in and
around the clusters on 10-14 Mpc scale to study the hierarchical growth of
clusters through assembly of surrounding groups. (2) Investigating the
environmental variation of galaxy properties along the structures to study the
origin of the morphology-density and star formation-density relations. Some
initial results are presented. On galactic scale, we first present the stellar
mass growth of cluster galaxies out to z~1.5 based on the near-infrared imaging
of distant clusters and show that the mass assembly process of galaxies is
largely completed by z~1.5 and is faster than the current semi-analytic models'
predictions. We then focus on the faint end of the luminosity function at z~1
based on the Subaru/XMM-Newton Deep Survey imaging data. We show the deficit of
red galaxies below M*+2 or 10^{10} Msun, which suggest less massive galaxies
are either genuinely young or still vigorously forming stars in sharp contrast
to the massive galaxies where mass is assembled and star formation is
terminated long time ago.Comment: To appear in the proceedings of IAU colloq. No. 195, "Outskirts of
Galaxy Clusters: intense life in the suburbs", Torino, 12-16 March 2004, 7
pages, 7 figures, uses IAU macr
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