7,779 research outputs found
Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction
A Planck-scale minimal observable length appears in many approaches to
quantum gravity. It is sometimes argued that this minimal length might conflict
with Lorentz invariance, because a boosted observer could see the minimal
length further Lorentz contracted. We show that this is not the case within
loop quantum gravity. In loop quantum gravity the minimal length (more
precisely, minimal area) does not appear as a fixed property of geometry, but
rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted
observer can see the same observable spectrum, with the same minimal area. What
changes continuously in the boost transformation is not the value of the
minimal length: it is the probability distribution of seeing one or the other
of the discrete eigenvalues of the area. We discuss several difficulties
associated with boosts and area measurement in quantum gravity. We compute the
transformation of the area operator under a local boost, propose an explicit
expression for the generator of local boosts and give the conditions under
which its action is unitary.Comment: 12 pages, 3 figure
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
Graviton propagator from background-independent quantum gravity
We study the graviton propagator in euclidean loop quantum gravity, using the
spinfoam formalism. We use boundary-amplitude and group-field-theory
techniques, and compute one component of the propagator to first order, under a
number of approximations, obtaining the correct spacetime dependence. In the
large distance limit, the only term of the vertex amplitude that contributes is
the exponential of the Regge action: the other terms, that have raised doubts
on the physical viability of the model, are suppressed by the phase of the
vacuum state, which is determined by the extrinsic geometry of the boundary.Comment: 6 pages. Substantially revised second version. Improved boundary
state ansat
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
The complete LQG propagator: II. Asymptotic behavior of the vertex
In a previous article we have show that there are difficulties in obtaining
the correct graviton propagator from the loop-quantum-gravity dynamics defined
by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude
that depends nontrivially on the intertwiners can yield the correct propagator.
We give an explicit example of asymptotic behavior of a vertex amplitude that
gives the correct full graviton propagator in the large distance limit.Comment: 16 page
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
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
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
- …