9,252 research outputs found
The century of the incomplete revolution: searching for general relativistic quantum field theory
In fundamental physics, this has been the century of quantum mechanics and
general relativity. It has also been the century of the long search for a
conceptual framework capable of embracing the astonishing features of the world
that have been revealed by these two ``first pieces of a conceptual
revolution''. I discuss the general requirements on the mathematics and some
specific developments towards the construction of such a framework. Examples of
covariant constructions of (simple) generally relativistic quantum field
theories have been obtained as topological quantum field theories, in
nonperturbative zero-dimensional string theory and its higher dimensional
generalizations, and as spin foam models. A canonical construction of a general
relativistic quantum field theory is provided by loop quantum gravity.
Remarkably, all these diverse approaches have turn out to be related,
suggesting an intriguing general picture of general relativistic quantum
physics.Comment: To appear in the Journal of Mathematical Physics 2000 Special Issu
Compatibility of radial, Lorenz and harmonic gauges
We observe that the radial gauge can be consistently imposed \emph{together}
with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge
in linearized general relativity. This simple observation has relevance for
some recent developments in quantum gravity where the radial gauge is
implicitly utilized.Comment: 9 pages, minor changes in the bibliograph
Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
The comprehensive formulation for loop quantum cosmology in the spatially
flat, isotropic model was recently constructed. In this paper, the methods are
extended to the anisotropic Bianchi I cosmology. Both the precursor and the
improved strategies are applied and the expected results are established: (i)
the scalar field again serves as an internal clock and is treated as emergent
time; (ii) the total Hamiltonian constraint is derived by imposing the
fundamental discreteness and gives the evolution as a difference equation; and
(iii) the physical Hilbert space, Dirac observables and semi-classical states
are constructed rigorously. It is also shown that the state in the kinematical
Hilbert space associated with the classical singularity is decoupled in the
difference evolution equation, indicating that the big bounce may take place
when any of the area scales undergoes the vanishing behavior. The investigation
affirms the robustness of the framework used in the isotropic model by
enlarging its domain of validity and provides foundations to conduct the
detailed numerical analysis.Comment: 53 pages, 2 figures; more typos corrected; HyperTeX enable
A simple background-independent hamiltonian quantum model
We study formulation and probabilistic interpretation of a simple
general-relativistic hamiltonian quantum system. The system has no unitary
evolution in background time. The quantum theory yields transition
probabilities between measurable quantities (partial observables). These
converge to the classical predictions in the limit. Our main tool
is the kernel of the projector on the solutions of Wheeler-deWitt equation,
which we analyze in detail. It is a real quantity, which can be seen as a
propagator that propagates "forward" as well as "backward" in a local parameter
time. Individual quantum states, on the other hand, may contain only "forward
propagating" components. The analysis sheds some light on the interpretation of
background independent transition amplitudes in quantum gravity
Relational evolution of the degrees of freedom of generally covariant quantum theories
We study the classical and quantum dynamics of generally covariant theories
with vanishing a Hamiltonian and with a finite number of degrees of freedom. In
particular, the geometric meaning of the full solution of the relational
evolution of the degrees of freedom is displayed, which means the determination
of the total number of evolving constants of motion required. Also a method to
find evolving constants is proposed. The generalized Heinsenberg picture needs
M time variables, as opposed to the Heisenberg picture of standard quantum
mechanics where one time variable t is enough. As an application, we study the
parameterized harmonic oscillator and the SL(2,R) model with one physical
degree of freedom that mimics the constraint structure of general relativity
where a Schrodinger equation emerges in its quantum dynamics.Comment: 25 pages, no figures, Latex file. Revised versio
Implications of the gauge-fixing in Loop Quantum Cosmology
The restriction to invariant connections in a Friedmann-Robertson-Walker
space-time is discussed via the analysis of the Dirac brackets associated with
the corresponding gauge fixing. This analysis allows us to establish the proper
correspondence between reduced and un-reduced variables. In this respect, it is
outlined how the holonomy-flux algebra coincides with the one of Loop Quantum
Gravity if edges are parallel to simplicial vectors and the quantization of the
model is performed via standard techniques by restricting admissible paths.
Within this scheme, the discretization of the area spectrum is emphasized.
Then, the role of the diffeomorphisms generator in reduced phase-space is
investigated and it is clarified how it implements homogeneity on quantum
states, which are defined over cubical knots. Finally, the perspectives for a
consistent dynamical treatment are discussed.Comment: 7 pages, accepted for publication in Physical Review
The Evolution of Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
Using the improved quantization technique to the mini-superspace
approximation of loop quantum gravity, we study the evolution of black holes
supported by a cosmological constant. The addition of a cosmological constant
allows for classical solutions with planar, cylindrical, toroidal and higher
genus black holes. Here we study the quantum analog of these space-times. In
all scenarios studied, the singularity present in the classical counter-part is
avoided in the quantized version and is replaced by a bounce, and in the late
evolution, a series of less severe bounces. Interestingly, although there are
differences during the evolution between the various symmetries and topologies,
the evolution on the other side of the bounce asymptotes to space-times of
Nariai-type, with the exception of the planar black hole analyzed here, whose
-=constant subspaces seem to continue expanding in the long term
evolution. For the other cases, Nariai-type universes are attractors in the
quantum evolution, albeit with different parameters. We study here the quantum
evolution of each symmetry in detail.Comment: 26 pages, 7 figures.V2 has typos corrected, references added, and a
more careful analysis of the planar case. Accepted for publication in
Physical Review
Local spinfoam expansion in loop quantum cosmology
The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and
Bianchi I models defined by loop quantum cosmology have recently been
translated into a spinfoam-like formalism. The construction is facilitated by
the presence of a massless scalar field which is used as an internal clock. The
implicit integration over the matter variable leads to a nonlocal spinfoam
amplitude. In this paper we consider a vacuum Bianchi I universe and show that
by choosing an appropriate regulator a spinfoam expansion can be obtained
without selecting a clock variable and that the resulting spinfoam amplitude is
local.Comment: 12 page
Loop quantum cosmology and the k = - 1 RW model
The loop quantization of the negatively curved k=-1 RW model poses several
technical challenges. We show that the issues can be overcome and a successful
quantization is possible that extends the results of the k=0,+1 models in a
natural fashion. We discuss the resulting dynamics and show that for a universe
consisting of a massless scalar field, a bounce is predicted in the backward
evolution in accordance with the results of the k=0,+1 models. We also show
that the model predicts a vacuum repulsion in the high curvature regime that
would lead to a bounce even for matter with vanishing energy density. We
finally comment on the inverse volume modifications of loop quantum cosmology
and show that, as in the k=0 model, the modifications depend sensitively on the
introduction of a length scale which a priori is independent of the curvature
scale or a matter energy scale.Comment: Clarified some of the discussion and updated reference
Physics with nonperturbative quantum gravity: radiation from a quantum black hole
We study quantum gravitational effects on black hole radiation, using loop
quantum gravity. Bekenstein and Mukhanov have recently considered the
modifications caused by quantum gravity on Hawking's thermal black-hole
radiation. Using a simple ansatz for the eigenstates the area, they have
obtained the intriguing result that the quantum properties of geometry affect
the radiation considerably, yielding a definitely non-thermal spectrum. Here,
we replace the simple ansatz employed by Bekenstein and Mukhanov with the
actual eigenstates of the area, computed using the loop representation of
quantum gravity. We derive the emission spectra, using a classic result in
number theory by Hardy and Ramanujan. Disappointingly, we do not recover the
Bekenstein-Mukhanov spectrum, but --effectively-- a Hawking's thermal spectrum.
The Bekenstein-Mukhanov result is therefore likely to be an artefact of the
naive ansatz, rather than a robust result. The result is an example of concrete
(although somewhat disappointing) application of nonperturbative quantum
gravity.Comment: 4 pages, latex-revtex, no figure
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