6,467 research outputs found
Physical effects of the Immirzi parameter
The Immirzi parameter is a constant appearing in the general relativity
action used as a starting point for the loop quantization of gravity. The
parameter is commonly believed not to show up in the equations of motion,
because it appears in front of a term in the action that vanishes on shell. We
show that in the presence of fermions, instead, the Immirzi term in the action
does not vanish on shell, and the Immirzi parameter does appear in the
equations of motion. It determines the coupling constant of a four-fermion
interaction. Therefore the Immirzi parameter leads to effects that are
observable in principle, even independently from nonperturbative quantum
gravity.Comment: 3 pages. Substantial revision from the first versio
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
Multiple-event probability in general-relativistic quantum mechanics
We discuss the definition of quantum probability in the context of "timeless"
general--relativistic quantum mechanics. In particular, we study the
probability of sequences of events, or multi-event probability. In conventional
quantum mechanics this can be obtained by means of the ``wave function
collapse" algorithm. We first point out certain difficulties of some natural
definitions of multi-event probability, including the conditional probability
widely considered in the literature. We then observe that multi-event
probability can be reduced to single-event probability, by taking into account
the quantum nature of the measuring apparatus. In fact, by exploiting the
von-Neumann freedom of moving the quantum classical boundary, one can always
trade a sequence of non-commuting quantum measurements at different times, with
an ensemble of simultaneous commuting measurements on the joint
system+apparatus system. This observation permits a formulation of quantum
theory based only on single-event probability, where the results of the "wave
function collapse" algorithm can nevertheless be recovered. The discussion
bears also on the nature of the quantum collapse
The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
Some components of the graviton two-point function have been recently
computed in the context of loop quantum gravity, using the spinfoam
Barrett-Crane vertex. We complete the calculation of the remaining components.
We find that, under our assumptions, the Barrett-Crane vertex does not yield
the correct long distance limit. We argue that the problem is general and can
be traced to the intertwiner-independence of the Barrett-Crane vertex, and
therefore to the well-known mismatch between the Barrett-Crane formalism and
the standard canonical spin networks. In a companion paper we illustrate the
asymptotic behavior of a vertex amplitude that can correct this difficulty.Comment: 31 page
The loop-quantum-gravity vertex-amplitude
Spinfoam theories are hoped to provide the dynamics of non-perturbative loop
quantum gravity. But a number of their features remain elusive. The best
studied one -the euclidean Barrett-Crane model- does not have the boundary
state space needed for this, and there are recent indications that,
consequently, it may fail to yield the correct low-energy -point functions.
These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way
certain second class constraints are imposed, arguably incorrectly, strongly.
We present an alternative model, that can be derived as a bona fide
quantization of a Regge discretization of euclidean general relativity, and
where the constraints are imposed weakly. Its state space is a natural subspace
of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network
space. The model provides a long sought SO(4)-covariant vertex amplitude for
loop quantum gravity.Comment: 6page
3+1 spinfoam model of quantum gravity with spacelike and timelike components
We present a spinfoam formulation of Lorentzian quantum General Relativity.
The theory is based on a simple generalization of an Euclidean model defined in
terms of a field theory over a group. The model is an extension of a recently
introduced Lorentzian model, in which both timelike and spacelike components
are included. The spinfoams in the model, corresponding to quantized
4-geometries, carry a natural non-perturbative local causal structure induced
by the geometry of the algebra of the internal gauge (sl(2,C)). Amplitudes can
be expressed as integrals over the spacelike unit-vectors hyperboloid in
Minkowski space, or the imaginary Lobachevskian space.Comment: 16 pages, 1 figur
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum
gravity, using the spinfoam formalism, up to some second order terms in the
expansion parameter.Comment: 41 pages, 6 figure
Three dimensional loop quantum gravity: physical scalar product and spin foam models
In this paper, we address the problem of the dynamics in three dimensional
loop quantum gravity with zero cosmological constant. We construct a rigorous
definition of Rovelli's generalized projection operator from the kinematical
Hilbert space--corresponding to the quantization of the infinite dimensional
kinematical configuration space of the theory--to the physical Hilbert space.
In particular, we provide the definition of the physical scalar product which
can be represented in terms of a sum over (finite) spin-foam amplitudes.
Therefore, we establish a clear-cut connection between the canonical
quantization of three dimensional gravity and spin-foam models. We emphasize
two main properties of the result: first that no cut-off in the kinematical
degrees of freedom of the theory is introduced (in contrast to standard
`lattice' methods), and second that no ill-defined sum over spins (`bubble'
divergences) are present in the spin foam representation.Comment: Typos corrected, version appearing in Class. Quant. Gra
On the Physical Hilbert Space of Loop Quantum Cosmology
In this paper we present a model of Riemannian loop quantum cosmology with a
self-adjoint quantum scalar constraint. The physical Hilbert space is
constructed using refined algebraic quantization. When matter is included in
the form of a cosmological constant, the model is exactly solvable and we show
explicitly that the physical Hilbert space is separable consisting of a single
physical state. We extend the model to the Lorentzian sector and discuss
important implications for standard loop quantum cosmology
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