152 research outputs found
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
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
Examination of the nature of the Bianchi type cosmological singularities
We present quantum (and classical) Bianchi I model, with free massless scalar
field, of the Universe. Our model may be treated as the simplest prototype of
the quantum BKL (Belinskii-Khalatnikov-Lifshitz) scenario. The quantization is
done by making use of the nonstandard Loop Quantum Cosmology (LQC). Since the
method is quite new, we present in details its motivation and the formalism. To
make the nonstandard method easily understandable, we include its application
to the FRW model. In the nonstandard LQC, we first solve the Hamiltonian
constraint of the theory at the classical level and find elementary
observables. Physical compound observables are defined in terms of elementary
ones. We find that classical Big Bang singularity is replaced by quantum Big
Bounce transition due to modification of classical theory by holonomy around a
loop with finite size. The energy density of matter fields at the Big Bounce
depends on a free parameter {\lambda}, which value is expected to be determined
from future cosmological observations. The phase space is divided into two
distinct regions: Kasner-like and Kasner-unlike. We use the elementary
observables to quantize volume and directional volume operators in both cases.
Spectra of these operators are bounded from below and discrete, and depend on
{\lambda}. The discreteness may imply a foamy structure of spacetime at
semiclassical level. At the quantum level an evolution of the model is
generated by the so-called true Hamiltonian. This enables introducing a time
parameter valued in the set of all real numbers.Comment: This is my PhD Thesis, about 80 page
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
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