259 research outputs found
How to detect an anti-spacetime
Is it possible, in principle, to measure the sign of the Lapse? We show that
fermion dynamics distinguishes spacetimes having the same metric but different
tetrads, for instance a Lapse with opposite sign. This sign might be a physical
quantity not captured by the metric. We discuss its possible role in quantum
gravity.Comment: Article awarded with an "Honorable Mention" from the 2012 Gravity
Foundation Award. 6 pages, 8 (pretty) figure
From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model
A Kaluza-Klein like approach for a 4d spin foam model is considered. By
applying this approach to a model based on group field theory in 4d (TOCY
model), and using the Peter-Weyl expansion of the gravitational field,
reconstruction of new non gravitational fields and interactions in the action
are found. The perturbative expansion of the partition function produces graphs
colored with su(2) algebraic data, from which one can reconstruct a 3d
simplicial complex representing space-time and its geometry; (like in the
Ponzano-Regge formulation of pure 3d quantum gravity), as well as the Feynman
graph for typical matter fields. Thus a mechanism for generation of matter and
construction of new dimensions are found from pure gravity.Comment: 11 pages, no figure, to be published in International Journal of
Geometric Methods in Modern Physic
Semiclassical Analysis of the Wigner Symbol with One Small Angular Momentum
We derive an asymptotic formula for the Wigner symbol, in the limit of
one small and 11 large angular momenta. There are two kinds of asymptotic
formulas for the symbol with one small angular momentum. We present the
first kind of formula in this paper. Our derivation relies on the techniques
developed in the semiclassical analysis of the Wigner symbol [L. Yu and R.
G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant
form of the multicomponent WKB wave-functions to derive asymptotic formulas for
the symbol with small and large angular momenta. When applying the same
technique to the symbol in this paper, we find that the spinor is
diagonalized in the direction of an intermediate angular momentum. In addition,
we find that the geometry of the derived asymptotic formula for the
symbol is expressed in terms of the vector diagram for a symbol. This
illustrates a general geometric connection between asymptotic limits of the
various symbols. This work contributes the first known asymptotic formula
for the symbol to the quantum theory of angular momentum, and serves as a
basis for finding asymptotic formulas for the Wigner symbol with two
small angular momenta.Comment: 15 pages, 14 figure
3-dimensional Gravity from the Turaev-Viro Invariant
We study the -deformed su(2) spin network as a 3-dimensional quantum
gravity model. We show that in the semiclassical continuum limit the
Turaev-Viro invariant obtained recently defines naturally regularized
path-integral la Ponzano-Regge, In which a contribution from
the cosmological term is effectively included. The regularization dependent
cosmological constant is found to be , where
. We also discuss the relation to the Euclidean Chern-Simons-Witten
gravity in 3-dimension.Comment: 11page
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
Holography for the Lorentz Group Racah Coefficients
A known realization of the Lorentz group Racah coefficients is given by an
integral of a product of 6 ``propagators'' over 4 copies of the hyperbolic
space. These are ``bulk-to-bulk'' propagators in that they are functions of two
points in the hyperbolic space. It is known that the bulk-to-bulk propagator
can be constructed out of two bulk-to-boundary ones. We point out that there is
another way to obtain the same object. Namely, one can use two bulk-to-boundary
and one boundary-to-boundary propagator. Starting from this construction and
carrying out the bulk integrals we obtain a realization of the Racah
coefficients that is ``holographic'' in the sense that it only involves
boundary objects. This holographic realization admits a geometric
interpretation in terms of an ``extended'' tetrahedron.Comment: 12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron
interpretation adde
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
Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity
The Turaev-Viro state sum invariant is known to give the transition amplitude
for the three dimensional BF theory with cosmological term, and its deformation
parameter hbar is related with the cosmological constant via hbar=sqrt{Lambda}.
This suggests a way to find the expectation value of the spacetime volume by
differentiating the Turaev-Viro amplitude with respect to the cosmological
constant. Using this idea, we find an explicit expression for the spacetime
volume in BF theory. According to our results, each labelled triangulation
carries a volume that depends on the labelling spins. This volume is explicitly
discrete. We also show how the Turaev-Viro model can be used to obtain the
spacetime volume for (2+1) dimensional quantum gravity.Comment: 13 pages, Revtex, figure
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
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
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