220 research outputs found
Abelian BF theory and Turaev-Viro invariant
The U(1) BF Quantum Field Theory is revisited in the light of
Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition
function is related to the BF one and how the latter on its turn coincides with
an abelian Turaev-Viro invariant. Significant differences compared to the
non-abelian case are highlighted.Comment: 47 pages and 6 figure
Semiclassical Analysis of the Wigner -Symbol with Small and Large Angular Momenta
We derive a new asymptotic formula for the Wigner -symbol, in the limit
of one small and eight large angular momenta, using a novel gauge-invariant
factorization for the asymptotic solution of a set of coupled wave equations.
Our factorization eliminates the geometric phases completely, using
gauge-invariant non-canonical coordinates, parallel transports of spinors, and
quantum rotation matrices. Our derivation generalizes to higher -symbols.
We display without proof some new asymptotic formulas for the -symbol and
the -symbol in the appendices. This work contributes a new asymptotic
formula of the Wigner -symbol to the quantum theory of angular momentum,
and serves as an example of a new general method for deriving asymptotic
formulas for -symbols.Comment: 18 pages, 16 figures. To appear in Phys. Rev.
N=2 supersymmetric spin foams in three dimensions
We construct the spin foam model for N=2 supergravity in three dimensions.
Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has
representations which are not completely reducible. This complicates the
procedure when building a state sum. Fortunately, one can and should excise
these representations. We show that the restricted subset of representations
form a subcategory closed under tensor product. The resulting state-sum is once
again a topological invariant. Furthermore, within this framework one can
identify positively and negatively charged fermions propagating on the spin
foam. These results on osp(2|2) representations and intertwiners apply more
generally to spin network states for N=2 loop quantum supergravity (in 3+1
dimensions) where it allows to define a notion of BPS states.Comment: 12 page
Observables in 3-dimensional quantum gravity and topological invariants
In this paper we report some results on the expectation values of a set of
observables introduced for 3-dimensional Riemannian quantum gravity with
positive cosmological constant, that is, observables in the Turaev-Viro model.
Instead of giving a formal description of the observables, we just formulate
the paper by examples. This means that we just show how an idea works with
particular cases and give a way to compute 'expectation values' in general by a
topological procedure.Comment: 24 pages, 47 figure
Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
We show that the -product for , group Fourier transform and
effective action arising in [1] in an effective theory for the integer spin
Ponzano-Regge quantum gravity model are compatible with the noncommutative
bicovariant differential calculus, quantum group Fourier transform and
noncommutative scalar field theory previously proposed for 2+1 Euclidean
quantum gravity using quantum group methods in [2]. The two are related by a
classicalisation map which we introduce. We show, however, that noncommutative
spacetime has a richer structure which already sees the half-integer spin
information. We argue that the anomalous extra `time' dimension seen in the
noncommutative geometry should be viewed as the renormalisation group flow
visible in the coarse-graining in going from to . Combining our
methods we develop practical tools for noncommutative harmonic analysis for the
model including radial quantum delta-functions and Gaussians, the Duflo map and
elements of `noncommutative sampling theory'. This allows us to understand the
bandwidth limitation in 2+1 quantum gravity arising from the bounded
momentum and to interpret the Duflo map as noncommutative compression. Our
methods also provide a generalised twist operator for the -product.Comment: 53 pages latex, no figures; extended the intro for this final versio
Spin Foam Diagrammatics and Topological Invariance
We provide a simple proof of the topological invariance of the Turaev-Viro
model (corresponding to simplicial 3d pure Euclidean gravity with cosmological
constant) by means of a novel diagrammatic formulation of the state sum models
for quantum BF-theories. Moreover, we prove the invariance under more general
conditions allowing the state sum to be defined on arbitrary cellular
decompositions of the underlying manifold. Invariance is governed by a set of
identities corresponding to local gluing and rearrangement of cells in the
complex. Due to the fully algebraic nature of these identities our results
extend to a vast class of quantum groups. The techniques introduced here could
be relevant for investigating the scaling properties of non-topological state
sums, being proposed as models of quantum gravity in 4d, under refinement of
the cellular decomposition.Comment: 20 pages, latex with AMS macros and eps figure
Relating Covariant and Canonical Approaches to Triangulated Models of Quantum Gravity
In this paper explore the relation between covariant and canonical approaches
to quantum gravity and theory. We will focus on the dynamical
triangulation and spin-foam models, which have in common that they can be
defined in terms of sums over space-time triangulations. Our aim is to show how
we can recover these covariant models from a canonical framework by providing
two regularisations of the projector onto the kernel of the Hamiltonian
constraint. This link is important for the understanding of the dynamics of
quantum gravity. In particular, we will see how in the simplest dynamical
triangulations model we can recover the Hamiltonian constraint via our
definition of the projector. Our discussion of spin-foam models will show how
the elementary spin-network moves in loop quantum gravity, which were
originally assumed to describe the Hamiltonian constraint action, are in fact
related to the time-evolution generated by the constraint. We also show that
the Immirzi parameter is important for the understanding of a continuum limit
of the theory.Comment: 28 pages, 10 figure
Asymptotics of LQG fusion coefficients
The fusion coefficients from SO(3) to SO(4) play a key role in the definition
of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we
give a simple analytic formula of the EPRL fusion coefficients. We study the
large spin asymptotics and show that they map SO(3) semiclassical intertwiners
into semiclassical intertwiners. This non-trivial
property opens the possibility for an analysis of the semiclassical behavior of
the model.Comment: 14 pages, minor change
Not all forms of muscle hypertonia worsen with fatigue. A pilot study in para swimmers
In hypertonic muscles of patients with upper motor neuron syndrome (UMNS), investigation with surface electromyography (EMG) with the muscle in a shortened position and during passive muscle stretch allows to identify two patterns underlying hypertonia: spasticity and spastic dystonia. We recently observed in Para swimmers that the effect of fatigue on hypertonia can be different from subject to subject. Our goal was, therefore, to understand whether this divergent behavior may depend on the specific EMG pattern underlying hypertonia. We investigated eight UMNS Para swimmers (five men, mean age 23.25 ± 3.28 years), affected by cerebral palsy, who presented muscle hypertonia of knee flexors and extensors. Muscle tone was rated using the Modified Ashworth Scale (MAS). EMG patterns were investigated in rectus femoris (RF) and biceps femoris (BF) before and after two fatiguing motor tasks of increasing intensity. Before the fatiguing tasks, two subjects (#2 and 7) had spasticity and one subject (#5) had spastic dystonia in both RF and BF. Two subjects (#3 and 4) showed spasticity in RF and spastic dystonia in BF, whereas one subject (#1) had spasticity in RF and no EMG activity in BF. The remaining two subjects (#6 and 8) had spastic dystonia in RF and no EMG activity in BF. In all the 16 examined muscles, these EMG patterns persisted after the fatiguing tasks. Spastic dystonia increased (p < 0.05), while spasticity did not change (p > 0.05). MAS scores increased only in the muscles affected by spastic dystonia. Among the phenomena possibly underlying hypertonia, only spastic dystonia is fatigue-dependent. Technical staff and medical classifiers should be aware of this specificity, because, in athletes with spastic dystonia, intense and prolonged motor activity could negatively affect competitive performance, creating a situation of unfairness among Para athletes belonging to the same sports class
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