116 research outputs found
SO_0(1,d+1) Racah coefficients: Type I representations
We use AdS/CFT inspired methods to study the Racah coefficients for type I
representations of the Lorentz group SO_0(1,d+1) with d>1. For such
representations (a multiple of) the Racah coefficient can be represented as an
integral of a product of 6 bulk-to-bulk propagators over 4 copies of the
hyperbolic space H_{d+1}. To compute the integrals we represent the
bulk-to-bulk propagators in terms of bulk-to-boundary ones. The bulk integrals
can be computed explicitly, and the boundary integrations are carried out by
introducing Feynman parameters. The final result is an integral representation
of the Racah coefficient given by 4 Barnes-Mellin type integrals.Comment: 20 pages, 1 figure. v2: Case d=1 corrected, case d>1 clarifie
Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
We consider the Lie group generated by the Lie algebra
of -Minkowski space. Imposing the invariance of the metric under the
pull-back of diffeomorphisms induced by right translations in the group, we
show that a unique right invariant metric is associated with
. This metric coincides with the metric of de Sitter
space-time. We analyze the structure of unitary representations of the group
relevant for the realization of the non-commutative
-Minkowski space by embedding into -dimensional Heisenberg
algebra. Using a suitable set of generalized coherent states, we select the
particular Hilbert space and realize the non-commutative -Minkowski
space as an algebra of the Hilbert-Schmidt operators. We define dequantization
map and fuzzy variant of the Laplace-Beltrami operator such that dequantization
map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami
operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der
Physik by a note and references added and adjuste
Relating Spin Foams and Canonical Quantum Gravity: A Discrete Step Evolution Formulation of Spin Foams
This article has been replaced by gr-qc/0412011Comment: This article has been replaced by gr-qc/041201
Contracted Representation of Yang's Space-Time Algebra and Buniy-Hsu-Zee's Discrete Space-Time
Motivated by the recent proposition by Buniy, Hsu and Zee with respect to
discrete space-time and finite spatial degrees of freedom of our physical world
with a short- and a long-distance scales, and we reconsider the
Lorentz-covariant Yang's quantized space-time algebra (YSTA), which is
intrinsically equipped with such two kinds of scale parameters, and
. In accordance with their proposition, we find the so-called contracted
representation of YSTA with finite spatial degrees of freedom associated with
the ratio , which gives a possibility of the divergence-free
noncommutative field theory on YSTA. The canonical commutation relations
familiar in the ordinary quantum mechanics appear as the cooperative
Inonu-Wigner's contraction limit of YSTA, and $R \to \infty.
Two Dimensional Fractional Supersymmetry from the Quantum Poincare Group at Roots of Unity
A group theoretical understanding of the two dimensional fractional
supersymmetry is given in terms of the quantum Poincare group at roots of
unity. The fractional supersymmetry algebra and the quantum group dual to it
are presented and the pseudo-unitary, irreducible representations of them are
obtained. The matrix elements of these representations are explicitly
constructed.Comment: 10 pages. Some misprints are corrected. To appear in J. Phys.
A minimal approach for the local statistical properties of a one-dimensional disordered wire
We consider a one-dimensional wire in gaussian random potential. By treating
the spatial direction as imaginary time, we construct a `minimal'
zero-dimensional quantum system such that the local statistical properties of
the wire are given as products of statistically independent matrix elements of
the evolution operator of the system. The space of states of this quantum
system is found to be a particular non-unitary, infinite dimensional
representation of the pseudo-unitary group, U(1,1). We show that our
construction is minimal in a well defined sense, and compare it to the
supersymmetry and Berezinskii techniques.Comment: 10 pages, 0 figure
Quantum particle on hyperboloid
We present quantization of particle dynamics on one-sheet hyperboloid
embedded in three dimensional Minkowski space. Taking account of all global
symmetries enables unique quantization. Making use of topology of canonical
variables not only simplifies calculations but also gives proper framework for
analysis.Comment: 7 pages, no figures, revtex
Group-theoretical approach to a non-central extension of the Kepler-Coulomb problem
Bound and scattering states of a non-central extension of the
three-dimensional Kepler-Coulomb Hamiltonian are worked out analytically within
the framework of the potential groups of the problem, SO(7) for bound states
and SO(6,1) for scattering states. In the latter case, the S matrix is
calculated by the method of intertwining operators.Comment: 12 pages, to appear in J. Phys. A : Math. Theo
Gravitational Wilson Loop and Large Scale Curvature
In a quantum theory of gravity the gravitational Wilson loop, defined as a
suitable quantum average of a parallel transport operator around a large
near-planar loop, provides important information about the large-scale
curvature properties of the geometry. Here we shows that such properties can be
systematically computed in the strong coupling limit of lattice regularized
quantum gravity, by performing a local average over rotations, using an assumed
near-uniform measure in group space. We then relate the resulting quantum
averages to an expected semi-classical form valid for macroscopic observers,
which leads to an identification of the gravitational correlation length
appearing in the Wilson loop with an observed large-scale curvature. Our
results suggest that strongly coupled gravity leads to a positively curved (De
Sitter-like) quantum ground state, implying a positive effective cosmological
constant at large distances.Comment: 22 pages, 6 figure
Evolution Equation for Generalized Parton Distributions
The extension of the method [arXiv:hep-ph/0503109] for solving the leading
order evolution equation for Generalized Parton Distributions (GPDs) is
presented. We obtain the solution of the evolution equation both for the flavor
nonsinglet quark GPD and singlet quark and gluon GPDs. The properties of the
solution and, in particular, the asymptotic form of GPDs in the small x and \xi
region are discussed.Comment: REVTeX4, 34 pages, 3 figure
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