73,743 research outputs found
Loop Quantum Gravity
The problem of finding the quantum theory of the gravitational field, and
thus understanding what is quantum spacetime, is still open. One of the most
active of the current approaches is loop quantum gravity. Loop quantum gravity
is a mathematically well-defined, non-perturbative and background independent
quantization of general relativity, with its conventional matter couplings. The
research in loop quantum gravity forms today a vast area, ranging from
mathematical foundations to physical applications. Among the most significative
results obtained are: (i) The computation of the physical spectra of
geometrical quantities such as area and volume; which yields quantitative
predictions on Planck-scale physics. (ii) A derivation of the
Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical
picture of the microstructure of quantum physical space, characterized by a
polymer-like Planck scale discreteness. This discreteness emerges naturally
from the quantum theory and provides a mathematically well-defined realization
of Wheeler's intuition of a spacetime ``foam''. Long standing open problems
within the approach (lack of a scalar product, overcompleteness of the loop
basis, implementation of reality conditions) have been fully solved. The weak
part of the approach is the treatment of the dynamics: at present there exist
several proposals, which are intensely debated. Here, I provide a general
overview of ideas, techniques, results and open problems of this candidate
theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34
page
Testing loop quantum cosmology
Loop quantum cosmology predicts that quantum gravity effects resolve the
big-bang singularity and replace it by a cosmic bounce. Furthermore, loop
quantum cosmology can also modify the form of primordial cosmological
perturbations, for example by reducing power at large scales in inflationary
models or by suppressing the tensor-to-scalar ratio in the matter bounce
scenario; these two effects are potential observational tests for loop quantum
cosmology. In this article, I review these predictions and others, and also
briefly discuss three open problems in loop quantum cosmology: its relation to
loop quantum gravity, the trans-Planckian problem, and a possible transition
from a Lorentzian to a Euclidean space-time around the bounce point.Comment: 20 pages. Invited review for special edition "Testing quantum gravity
with cosmology" of Comptes Rendus Physiqu
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
We present an introduction to the canonical quantization of gravity performed
in loop quantum gravity, based on lectures held at the 3rd quantum geometry and
quantum gravity school in Zakopane in 2011. A special feature of this
introduction is the inclusion of new proposals for coupling matter to gravity
that can be used to deparametrize the theory, thus making its dynamics more
tractable. The classical and quantum aspects of these new proposals are
explained alongside the standard quantization of vacuum general relativity in
loop quantum gravity.Comment: 56 pages. Contribution to the Proceedings of the 3rd Quantum Geometry
and Quantum Gravity School in Zakopane (2011). v2: Typos corrected, various
small changes in presentation, version as published in Po
Spin foam models with finite groups
Spin foam models, loop quantum gravity and group field theory are discussed
as quantum gravity candidate theories and usually involve a continuous Lie
group. We advocate here to consider quantum gravity inspired models with finite
groups, firstly as a test bed for the full theory and secondly as a class of
new lattice theories possibly featuring an analogue diffeomorphism symmetry. To
make these notes accessible to readers outside the quantum gravity community we
provide an introduction to some essential concepts in the loop quantum gravity,
spin foam and group field theory approach and point out the many connections to
lattice field theory and condensed matter systems.Comment: 47 pages, 6 figure
Quantum self-gravitating collapsing matter in a quantum geometry
The problem of how space-time responds to gravitating quantum matter in full
quantum gravity has been one of the main questions that any program of
quantization of gravity should address. Here we analyze this issue by
considering the quantization of a collapsing null shell coupled to spherically
symmetric loop quantum gravity. We show that the constraint algebra of
canonical gravity is Abelian both classically and when quantized using loop
quantum gravity techniques. The Hamiltonian constraint is well defined and
suitable Dirac observables characterizing the problem were identified at the
quantum level. We can write the metric as a parameterized Dirac observable at
the quantum level and study the physics of the collapsing shell and black hole
formation. We show how the singularity inside the black hole is eliminated by
loop quantum gravity and how the shell can traverse it. The construction is
compatible with a scenario in which the shell tunnels into a baby universe
inside the black hole or one in which it could emerge through a white hole.Comment: 4 pages, RevTe
- …