8,657 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 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

### Towards Loop Quantum Gravity without the time gauge

The Hamiltonian formulation of the Holst action is reviewed and it is
provided a solution of second-class constraints corresponding to a generic
local Lorentz frame. Within this scheme the form of rotation constraints can be
reduced to a Gauss-like one by a proper generalization of
Ashtekar-Barbero-Immirzi connections. This result emphasizes that the Loop
Quantum Gravity quantization procedure can be applied when the time-gauge
condition does not stand.Comment: 5 pages, accepted for publication in Phys. Rev. Let

### 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

### Reduced Phase Space Quantization and Dirac Observables

In her recent work, Dittrich generalized Rovelli's idea of partial
observables to construct Dirac observables for constrained systems to the
general case of an arbitrary first class constraint algebra with structure
functions rather than structure constants. Here we use this framework and
propose a new way for how to implement explicitly a reduced phase space
quantization of a given system, at least in principle, without the need to
compute the gauge equivalence classes. The degree of practicality of this
programme depends on the choice of the partial observables involved. The
(multi-fingered) time evolution was shown to correspond to an automorphism on
the set of Dirac observables so generated and interesting representations of
the latter will be those for which a suitable preferred subgroup is realized
unitarily. We sketch how such a programme might look like for General
Relativity. We also observe that the ideas by Dittrich can be used in order to
generate constraints equivalent to those of the Hamiltonian constraints for
General Relativity such that they are spatially diffeomorphism invariant. This
has the important consequence that one can now quantize the new Hamiltonian
constraints on the partially reduced Hilbert space of spatially diffeomorphism
invariant states, just as for the recently proposed Master constraint
programme.Comment: 18 pages, no figure

### Averaged null energy condition in Loop Quantum Cosmology

Wormhole and time machine are very interesting objects in general relativity.
However, they need exotic matters which are impossible in classical level to
support them. But if we introduce the quantum effects of gravity into the
stress-energy tensor, these peculiar objects can be constructed
self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential
to serve as a bridge connecting the classical theory and quantum gravity.
Therefore it provides a simple way for the study of quantum effect in the
semiclassical case. As is well known, loop quantum cosmology is very successful
to deal with the behavior of early universe. In the early stage, if taken the
quantum effect into consideration, inflation is natural because of the
violation of every kind of local energy conditions. Similar to the inflationary
universe, the violation of the averaged null energy condition is the necessary
condition for the traversable wormholes. In this paper, we investigate the
averaged null energy condition in LQC in the framework of effective
Hamiltonian, and find out that LQC do violate the averaged null energy
condition in the massless scalar field coupled model.Comment: 5 page

### Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology

We give a prescription to define in Loop Quantum Gravity the electric field
operator related to the scale factor of an homogeneous and isotropic
cosmological space-time. This procedure allows to link the fundamental theory
with its cosmological implementation. In view of the conjugate relation
existing between holonomies and fluxes, the edge length and the area of
surfaces in the fiducial metric satisfy a duality condition. As a consequence,
the area operator has a discrete spectrum also in Loop Quantum Cosmology. This
feature makes the super-Hamiltonian regularization an open issue of the whole
formulation.Comment: 4 pages, accepted for publication in Phys. Rev. D as a Rapid
Communicatio

### Strings as perturbations of evolving spin-networks

A connection between non-perturbative formulations of quantum gravity and
perturbative string theory is exhibited, based on a formulation of the
non-perturbative dynamics due to Markopoulou. In this formulation the dynamics
of spin network states and their generalizations is described in terms of
histories which have discrete analogues of the causal structure and many
fingered time of Lorentzian spacetimes. Perturbations of these histories turn
out to be described in terms of spin systems defined on 2-dimensional timelike
surfaces embedded in the discrete spacetime. When the history has a classical
limit which is Minkowski spacetime, the action of the perturbation theory is
given to leading order by the spacetime area of the surface, as in bosonic
string theory. This map between a non-perturbative formulation of quantum
gravity and a 1+1 dimensional theory generalizes to a large class of theories
in which the group SU(2) is extended to any quantum group or supergroup. It is
argued that a necessary condition for the non-perturbative theory to have a
good classical limit is that the resulting 1+1 dimensional theory defines a
consistent and stable perturbative string theory.Comment: Latex, 18 pages, no figure

### Vertex Expansion for the Bianchi I model

A perturbative expansion of Loop Quantum Cosmological transitions amplitudes
of Bianchi I models is performed. Following the procedure outlined in [1,2] for
isotropic models, it is shown that the resulting expansion can be written in
the form of a series of amplitudes each with a fixed number of transitions
mimicking a spin foam expansion. This analogy is more complete than in the
isotropic case, since there are now the additional anisotropic degrees of
freedom which play the role of `colouring' of the spin foams. Furthermore, the
isotropic expansion is recovered by integrating out the anisotropies.Comment: 15 pages, 2 figure

### Black hole entropy: inside or out?

A trialogue. Ted, Don, and Carlo consider the nature of black hole entropy.
Ted and Carlo support the idea that this entropy measures in some sense ``the
number of black hole microstates that can communicate with the outside world.''
Don is critical of this approach, and discussion ensues, focusing on the
question of whether the first law of black hole thermodynamics can be
understood from a statistical mechanics point of view.Comment: 42 pages, contribution to proceedings of Peyresq

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