82 research outputs found
A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
We define and discuss classical and quantum gravity in 2+1 dimensions in the
Galilean limit. Although there are no Newtonian forces between massive objects
in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on
the topology of spacetime there are typically finitely many topological degrees
of freedom as well as topological interactions of Aharonov-Bohm type between
massive objects. In order to capture these topological aspects we consider a
two-fold central extension of the Galilei group whose Lie algebra possesses an
invariant and non-degenerate inner product. Using this inner product we define
Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group.
The particular extension of the Galilei group we consider is the classical
double of a much studied group, the extended homogeneous Galilei group, which
is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure
of the doubly extended Galilei group, and quantise the Chern-Simons theory
using a Hamiltonian approach. Many aspects of the quantum theory are determined
by the quantum double of the extended homogenous Galilei group, or Galilei
double for short. We study the representation theory of the Galilei double,
explain how associated braid group representations account for the topological
interactions in the theory, and briefly comment on an associated
non-commutative Galilean spacetime.Comment: 38 pages, 1 figure, references update
Super-extended noncommutative Landau problem and conformal symmetry
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an
arbitrary magnetic field, is considered, with particular attention paid to the
homogeneous case. The system has three different phases, depending on the
magnetic field. Due to supersymmetry, the boundary critical phase which
separates the sub- and super-critical cases can be viewed as a reduction to the
zero-energy eigensubspace. In the sub-critical phase the system is described by
the superextension of exotic Newton-Hooke symmetry, combined with the conformal
so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the
super-critical phase. In the critical phase the spin degrees of freedom are
frozen and supersymmetry disappears.Comment: 12 pages, references added, published versio
Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
A unified vision of the symmetric coupling of angular momenta and of the
quantum mechanical volume operator is illustrated. The focus is on the quantum
mechanical angular momentum theory of Wigner's 6j symbols and on the volume
operator of the symmetric coupling in spin network approaches: here, crucial to
our presentation are an appreciation of the role of the Racah sum rule and the
simplification arising from the use of Regge symmetry. The projective geometry
approach permits the introduction of a symmetric representation of a network of
seven spins or angular momenta. Results of extensive computational
investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International
Conference on Computational Science and Application
On two superintegrable nonlinear oscillators in N dimensions
We consider the classical superintegrable Hamiltonian system given by
, where U
is known to be the "intrinsic" oscillator potential on the Darboux spaces of
nonconstant curvature determined by the kinetic energy term T and parametrized
by {\lambda}. We show that H is Stackel equivalent to the free Euclidean
motion, a fact that directly provides a curved Fradkin tensor of constants of
motion for H. Furthermore, we analyze in terms of {\lambda} the three different
underlying manifolds whose geodesic motion is provided by T. As a consequence,
we find that H comprises three different nonlinear physical models that, by
constructing their radial effective potentials, are shown to be two different
nonlinear oscillators and an infinite barrier potential. The quantization of
these two oscillators and its connection with spherical confinement models is
briefly discussed.Comment: 11 pages; based on the contribution to the Manolo Gadella Fest-60
years-in-pucelandia, "Recent advances in time-asymmetric quantum mechanics,
quantization and related topics" hold in Valladolid (Spain), 14-16th july
201
On the linear forms of the Schrodinger equation
Generalizing the linearisation procedure used by Dirac and later by
L\'evy-Leblond, we derive the first-order non-relativistic wave equations for
particles of spin 1 and spin 3/2 starting from the Schrodinger equation
Planck 2015 results. XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources
We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest all-sky catalogue of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the Y5R500 estimates are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires. the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical and X-ray data-sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under- luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples
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