163 research outputs found
Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics
We analyze the quantum Bianchi I model in the setting of the nonstandard loop
quantum cosmology. Elementary observables are used to quantize the volume
operator. The spectrum of the volume operator is bounded from below and
discrete. The discreteness may imply a foamy structure of spacetime at
semiclassical level. The results are described in terms of a free parameter
specifying loop geometry to be determined in astro-cosmo observations. An
evolution of the quantum model is generated by the so-called true Hamiltonian,
which enables an introduction of a time parameter valued in the set of all real
numbers.Comment: 18 pages, version accepted for publication by Class. Quant. Gra
Quantum particle on hyperboloid
We present quantization of particle dynamics on one-sheet hyperboloid
embedded in three dimensional Minkowski space. Taking account of all global
symmetries enables unique quantization. Making use of topology of canonical
variables not only simplifies calculations but also gives proper framework for
analysis.Comment: 7 pages, no figures, revtex
Simple model of big-crunch/big-bang transition
We present classical and quantum dynamics of a test particle in the
compactified Milne space. Background spacetime includes one compact space
dimension undergoing contraction to a point followed by expansion. Quantization
consists in finding a self-adjoint representation of the algebra of particle
observables. Our model offers some insight into the nature of the cosmic
singularity.Comment: 17 pages, no figures, RevTeX4, accepted for publication in Class.
Quantum Gra
Dynamical Ambiguities in Singular Gravitational Field
We consider particle dynamics in singular gravitational field. In 2d
spacetime the system splits into two independent gravitational systems without
singularity. Dynamical integrals of each system define algebra, but
the corresponding symmetry transformations are not defined globally.
Quantization leads to ambiguity. By including singularity one can get the
global symmetry. Quantization in this case leads to unique quantum
theory.Comment: 7 pages, latex, no figures, submitted for publicatio
Turning Big Bang into Big Bounce: I. Classical Dynamics
The big bounce (BB) transition within a flat Friedmann-Robertson-Walker model
is analyzed in the setting of loop geometry underlying the loop cosmology. We
solve the constraint of the theory at the classical level to identify physical
phase space and find the Lie algebra of the Dirac observables. We express
energy density of matter and geometrical functions in terms of the observables.
It is the modification of classical theory by the loop geometry that is
responsible for BB. The classical energy scale specific to BB depends on a
parameter that should be fixed either by cosmological data or determined
theoretically at quantum level, otherwise the energy scale stays unknown.Comment: 14 pages, 1 figure, version accepted for publication in Physical
Review
Coherent state quantization of a particle in de Sitter space
We present a coherent state quantization of the dynamics of a relativistic
test particle on a one-sheet hyperboloid embedded in a three-dimensional
Minkowski space. The group SO_0(1,2) is considered to be the symmetry group of
the system. Our procedure relies on the choice of coherent states of the motion
on a circle. The coherent state realization of the principal series
representation of SO_0(1,2) seems to be a new result.Comment: Journal of Physics A: Mathematical and General, vol. 37, in pres
Propagation of a string across the cosmological singularity
Our results concern the transition of a quantum string through the
singularity of the compactified Milne (CM) space. We restrict our analysis to
the string winding around the compact dimension (CD) of spacetime. The CD
undergoes contraction to a point followed by re-expansion. We demonstrate that
both classical and quantum dynamics of considered string are well defined. Most
of presently available calculations strongly suggest that the singularity of a
time dependent orbifold is useless as a model of the cosmological singularity.
We believe that our results bring, to some extent, this claim into question.Comment: 9 pages, 2 figures, revtex4; version accepted for publication in
Class. Quantum Gra
Dirac quantization of membrane in time dependent orbifold
We present quantum theory of a membrane propagating in the vicinity of a time
dependent orbifold singularity. The dynamics of a membrane, with the parameters
space topology of a torus, winding uniformly around compact dimension of the
embedding spacetime is mathematically equivalent to the dynamics of a closed
string in a flat FRW spacetime. The construction of the physical Hilbert space
of a membrane makes use of the kernel space of self-adjoint constraint
operators. It is a subspace of the representation space of the constraints
algebra. There exist non-trivial quantum states of a membrane evolving across
the singularity.Comment: 16 pages, no figures, version accepted for publication in Journal of
High Energy Physic
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