404 research outputs found
What is Dynamics in Quantum Gravity?
The appearance of Hamiltonian constraint in the canonical formalism for
general relativity reflects the lack of a fixed external time. The dynamics of
general relativistic systems can be expressed with respect to an arbitrarily
chosen internal degree of freedom, the so called internal clock. We investigate
the way in which the choice of internal clock determines the quantum dynamics
and how much different quantum dynamics induced by different clocks are. We
develop our method of comparison by extending the Hamilton-Jacobi theory of
contact transformations to include a new type of transformations which
transform both the canonical variables and the internal clock. We employ our
method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain
semiclassical corrections to the classical dynamics, which depend on the choice
of internal clock. For a unique quantisation map we find the abundance of
inequivalent semiclassical corrections induced by quantum dynamics taking place
in different internal clocks. It follows that the concepts like minimal volume,
maximal curvature and the number of quantum bounces, often used to describe
quantum effects in cosmological models, depend on the choice of internal clock.Comment: 14 pages, 6 figure
Physical Hilbert Spaces in Quantum Gravity
We summarize our investigation of the extent to which the choice of internal
clock influences the dynamics in quantum models of gravity. Firstly, at the
classical level, we define an extension to the Hamilton-Jacobi theory of
contact transformations, which allows for transformations of time coordinates.
Secondly, at the quantum level, we employ the extended theory to separate the
quantum effects brought by the free choice of internal clock from those
originating from inequivalent quantization maps. Next, we show with two
examples two kinds of origin of the clock effect in quantum gravitational
systems.Comment: 6 pages, Proceedings of the 14th Marcel Grossmann Meeting (Rome, July
12-18, 2015
Probing the cosmological singularity with a particle
We examine the transition of a particle across the singularity of the
compactified Milne (CM) space. Quantization of the phase space of a particle
and testing the quantum stability of its dynamics are consistent to one
another. One type of transition of a quantum particle is described by a quantum
state that is continuous at the singularity. It indicates the existence of a
deterministic link between the propagation of a particle before and after
crossing the singularity. Regularization of the CM space leads to the dynamics
similar to the dynamics in the de Sitter space. The CM space is a promising
model to describe the cosmological singularity deserving further investigation
by making use of strings and membranes.Comment: 19 pages, 7 figures, revtex4, added references, 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
Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe
Following our previous paper, Bergeron et al, Smooth quantum dynamics of the
mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the
quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer
framework, we present a further analysis of the dynamical properties of the
model. Consistently with the deep quantum regime, we implement the harmonic
approximation of the anisotropy potential. We thus obtain manageable dynamical
equations. We study the quantum anisotropic oscillations during the bouncing
phase of the universe. Neglecting the backreaction from transitions between
quantum anisotropy states we obtain analytical results. In particular, we
identify a parameter which is associated with dynamical properties of the
quantum model and describes a sort of phase transition. Once the parameter
exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks
down. The application of the present result to a simple model of the Universe
indicates that the parameter indeed exceeds its critical value and that there
takes place a huge production of anisotropy at the bounce. This in turn must
lead to a sustained phase of accelerated expansion, an inflationary phase. The
quantitative inclusion of backreaction shall be examined in a follow-up paper
based on the vibronic approach.Comment: 32 pages, 9 figure
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