1,007 research outputs found
The 2+1 Kepler Problem and Its Quantization
We study a system of two pointlike particles coupled to three dimensional
Einstein gravity. The reduced phase space can be considered as a deformed
version of the phase space of two special-relativistic point particles in the
centre of mass frame. When the system is quantized, we find some possibly
general effects of quantum gravity, such as a minimal distances and a foaminess
of the spacetime at the order of the Planck length. We also obtain a
quantization of geometry, which restricts the possible asymptotic geometries of
the universe.Comment: 59 pages, LaTeX2e, 9 eps figure
Panel Discussion - Management of Eurasian watermilfoil in the United States using native insects: State regulatory and management issues
While researchers have evaluated the potential of native
insect herbivores to manage nonindigenous aquatic plant
species such as Eurasian watermilfoil (
Myriophyllum spicatum
L.), the practical matters of regulatory compliance and implementation
have been neglected. A panel of aquatic nuisance
species program managers from three state natural
resource management agencies (Minnesota, Vermont and
Washington) discussed their regulatory and policy concerns.
In addition, one ecological consultant attempting to market
one of the native insects to manage Eurasian watermilfoil
added his perspective on the special challenges of distributing
a native biological control agent for management of Eurasian
watermilfoil
Broad Absorption Line Variability in Radio-Loud Quasars
We investigate C IV broad absorption line (BAL) variability within a sample
of 46 radio-loud quasars (RLQs), selected from SDSS/FIRST data to include both
core-dominated (39) and lobe-dominated (7) objects. The sample consists
primarily of high-ionization BAL quasars, and a substantial fraction have large
BAL velocities or equivalent widths; their radio luminosities and
radio-loudness values span ~2.5 orders of magnitude. We have obtained 34 new
Hobby-Eberly Telescope (HET) spectra of 28 BAL RLQs to compare to earlier SDSS
data, and we also incorporate archival coverage (primarily dual-epoch SDSS) for
a total set of 78 pairs of equivalent width measurements for 46 BAL RLQs,
probing rest-frame timescales of ~80-6000 d (median 500 d). In general, only
modest changes in the depths of segments of absorption troughs are observed,
akin to those seen in prior studies of BAL RQQs. Also similar to previous
findings for RQQs, the RLQs studied here are more likely to display BAL
variability on longer rest-frame timescales. However, typical values of
|Delta_EW| and |Delta_EW|/ are about 40+/-20% lower for BAL RLQs when
compared with those of a timescale-matched sample of BAL RQQs. Optical
continuum variability is of similar amplitude in BAL RLQs and BAL RQQs; for
both RLQs and RQQs, continuum variability tends to be stronger on longer
timescales. BAL variability in RLQs does not obviously depend upon their radio
luminosities or radio-loudness values, but we do find tentative evidence for
greater fractional BAL variability within lobe-dominated RLQs. Enhanced BAL
variability within more edge-on (lobe-dominated) RLQs supports some geometrical
dependence to the outflow structure.Comment: 27 pages, 16 figures, 6 tables, accepted to MNRAS, full Appendix A at
http://www.macalester.edu/~bmille13/balrlqs.htm
(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
We formulate and analyze the Hamiltonian dynamics of a pair of massive
spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the
system to a conical infinity, isometric to the infinity generated by a single
massive but possibly spinning particle. The reduced phase space \Gamma_{red}
has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the
phase space of a Newtonian two-body system in the centre-of-mass frame, and we
find on \Gamma_{red} a canonical chart that makes this analogue explicit and
reduces to the Newtonian chart in the appropriate limit. Prospects for
quantization are commented on.Comment: 38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2:
Presentational improvement, references added, typos corrected.
Gravity in 2+1 dimensions as a Riemann-Hilbert problem
In this paper we consider 2+1-dimensional gravity coupled to N
point-particles. We introduce a gauge in which the - and
-components of the dreibein field become holomorphic and
anti-holomorphic respectively. As a result we can restrict ourselves to the
complex plane. Next we show that solving the dreibein-field: is
equivalent to solving the Riemann-Hilbert problem for the group . We
give the explicit solution for 2 particles in terms of hypergeometric
functions. In the N-particle case we give a representation in terms of
conformal field theory. The dreibeins are expressed as correlators of 2 free
fermion fields and twistoperators at the position of the particles.Comment: 32 pages Latex, 4 figures (uuencoded
Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in
the maximally slicing gauge has hamiltonian form. This is proved directly for
the two body problem and for the three body problem by using the Garnier
equations for isomonodromic transformations. For a number of particles greater
than three the existence of the hamiltonian is shown to be a consequence of a
conjecture by Polyakov which connects the auxiliary parameters of the fuchsian
differential equation which solves the SU(1,1) Riemann-Hilbert problem, to the
Liouville action of the conformal factor which describes the space-metric. We
give the exact diffeomorphism which transforms the expression of the spinning
cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing
gauge. It is explicitly shown that the boundary term in the action, written in
hamiltonian form gives the hamiltonian for the reduced particle dynamics. The
quantum mechanical translation of the two particle hamiltonian gives rise to
the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit
is given by the total energy of the system irrespective of the masses of the
particles thus proving at the quantum level a conjecture by 't Hooft on the two
particle dynamics. The quantum mechanical Green's function for the two body
problem is given.Comment: 34 pages LaTe
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