83 research outputs found
Unfashionable observations about three dimensional gravity
It is commonly accepted that the study of 2+1 dimensional quantum gravity
could teach us something about the 3+1 dimensional case. The non-perturbative
methods developed in this case share, as basic ingredient, a reformulation of
gravity as a gauge field theory. However, these methods suffer many problems.
Firstly, this perspective abandon the non-degeneracy of the metric and
causality as fundamental principles, hoping to recover them in a certain
low-energy limit. Then, it is not clear how these combinatorial techniques
could be used in the case where matter fields are added, which are however the
essential ingredients in order to produce non trivial observables in a
generally covariant approach. Endly, considering the status of the observer in
these approaches, it is not clear at all if they really could produce a
completely covariant description of quantum gravity. We propose to re-analyse
carefully these points. This study leads us to a really covariant description
of a set of self-gravitating point masses in a closed universe. This approach
is based on a set of observables associated to the measurements accessible to a
participant-observer, they manage to capture the whole dynamic in Chern-Simons
gravity as well as in true gravity. The Dirac algebra of these observables can
be explicitely computed, and exhibits interesting algebraic features related to
Poisson-Lie groupoids theory.Comment: 50 pages, written in LaTex, 3 pictures in encapsulated postscrip
Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
We analyze the hamiltonian quantization of Chern-Simons theory associated to
the universal covering of the Lorentz group SO(3,1). The algebra of observables
is generated by finite dimensional spin networks drawn on a punctured
topological surface. Our main result is a construction of a unitary
representation of this algebra. For this purpose, we use the formalism of
combinatorial quantization of Chern-Simons theory, i.e we quantize the algebra
of polynomial functions on the space of flat SL(2,C)-connections on a
topological surface with punctures. This algebra admits a unitary
representation acting on an Hilbert space which consists in wave packets of
spin-networks associated to principal unitary representations of the quantum
Lorentz group. This representation is constructed using only Clebsch-Gordan
decomposition of a tensor product of a finite dimensional representation with a
principal unitary representation. The proof of unitarity of this representation
is non trivial and is a consequence of properties of intertwiners which are
studied in depth. We analyze the relationship between the insertion of a
puncture colored with a principal representation and the presence of a
world-line of a massive spinning particle in de Sitter space.Comment: 78 pages. Packages include
Apport de la chirurgie mini-invasive dans le traitement des pathologies axiales traumatiques
Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
We consider non-chiral, full Lorentz group-based Plebanski formulation of
general relativity in its version that utilizes the Lagrange multiplier field
Phi with "internal" indices. The Hamiltonian analysis of this version of the
theory turns out to be simpler than in the previously considered in the
literature version with Phi carrying spacetime indices. We then extend the
Hamiltonian analysis to a more general class of theories whose action contains
scalars invariants constructed from Phi. Such theories have recently been
considered in the context of unification of gravity with other forces. We show
that these more general theories have six additional propagating degrees of
freedom as compared to general relativity, something that has not been
appreciated in the literature treating them as being not much different from
GR.Comment: 10 page
Three dimensional loop quantum gravity: coupling to point particles
We consider the coupling between three dimensional gravity with zero
cosmological constant and massive spinning point particles. First, we study the
classical canonical analysis of the coupled system. Then, we go to the
Hamiltonian quantization generalizing loop quantum gravity techniques. We give
a complete description of the kinematical Hilbert space of the coupled system.
Finally, we define the physical Hilbert space of the system of self-gravitating
massive spinning point particles using Rovelli's generalized projection
operator which can be represented as a sum over spin foam amplitudes. In
addition we provide an explicit expression of the (physical) distance operator
between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde
Canonical analysis of the BCEA topological matter model coupled to gravitation in (2+1) dimensions
We consider a topological field theory derived from the Chern - Simons action
in (2+1) dimensions with the I(ISO(2,1)) group,and we investigate in detail the
canonical structure of this theory.Originally developed as a topological theory
of Einstein gravity minimally coupled to topological matter fields in (2+1)
dimensions, it admits a BTZ black-hole solutions, and can be generalized to
arbitrary dimensions.In this paper, we further study the canonical structure of
the theory in (2+1) dimensions, by identifying all the distinct gauge
equivalence classes of solutions as they result from holonomy considerations.
The equivalence classes are discussed in detail, and examples of solutions
representative of each class are constructed or identified.Comment: 17 pages, no figure
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model
for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the
coherent state techniques introduced earlier in [arXiv:0705.0674], we show that
the EPR model realizes a consistent imposition of the simplicity constraints
implementing general relativity from a topological BF theory.Comment: 6 pages, 2 figures, v2: typos correcte
Benefits of repetitive transcranial magnetic stimulation (rTMS) for spastic subjects : clinical, functional and biomechanical parameters for lower limb and walking in five hemiparetic patients
Introduction. Spasticity is a disabling symptom resulting from reorganization of spinal reflexes no longer inhibited by supraspinal control. Several studies have demonstrated interest in repetitive transcranial magnetic stimulation in spastic patients. We conducted a prospective, randomized, double-blind crossover study on five spastic hemiparetic patients to determine whether this type of stimulation of the premotor cortex can provide a clinical benefit. Material and Methods. Two stimulation frequencies (1 Hz and 10 Hz) were tested versus placebo. Patients were assessed clinically, by quantitative analysis of walking and measurement of neuromechanical parameters (H and T reflexes, musculoarticular stiffness of the ankle). Results. No change was observed after placebo and 10 Hz protocols. Clinical parameters were not significantly modified after 1 Hz stimulation, apart from a tendency towards improved recruitment of antagonist muscles on the Fügl-Meyer scale. Only cadence and recurvatum were significantly modified on quantitative analysis of walking. Neuromechanical parameters were modified with significant decreases in Hmax / Mmaxand T/Mmax ratios and stiffness indices 9 days or 31 days after initiation of TMS. Conclusion. This preliminary study supports the efficacy of low-frequency TMS to reduce reflex excitability and stiffness of ankle plantar flexors, while clinical signs of spasticity were not significantly modified
Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model
We have calculated the large-q expansion for the energy cumulants and the
magnetization cumulants at the phase transition point in the two-dimensional
q-state Potts model to the 21st or 23rd order in using the finite
lattice method. The obtained series allow us to give very precise estimates of
the cumulants for on the first order transition point. The result
confirms us the correctness of the conjecture by Bhattacharya et al. on the
asymptotic behavior not only of the energy cumulants but also of the
magnetization cumulants for .Comment: 36 pages, LaTeX, 20 postscript figures, to appear in Nuclear Physics
Another weak first order deconfinement transition: three-dimensional SU(5) gauge theory
We examine the finite-temperature deconfinement phase transition of
(2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice
simulations. Unsurprisingly, we find that the transition is of first order,
however it appears to be weak. This fits naturally into the general picture of
"large" gauge groups having a first order deconfinement transition, even when
the center symmetry associated with the transition might suggest otherwise.Comment: 17 pages, 8 figure
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