53,149 research outputs found
The Quantum Modular Group in (2+1)-Dimensional Gravity
The role of the modular group in the holonomy representation of
(2+1)-dimensional quantum gravity is studied. This representation can be viewed
as a "Heisenberg picture", and for simple topologies, the transformation to the
ADM "Schr{\"o}dinger picture" may be found. For spacetimes with the spatial
topology of a torus, this transformation and an explicit operator
representation of the mapping class group are constructed. It is shown that the
quantum modular group splits the holonomy representation Hilbert space into
physically equivalent orthogonal ``fundamental regions'' that are interchanged
by modular transformations.Comment: 23 pages, LaTeX, no figures; minor changes and clarifications in
response to referee (basic argument and conclusions unaffected
Quantum geometry from 2+1 AdS quantum gravity on the torus
Wilson observables for 2+1 quantum gravity with negative cosmological
constant, when the spatial manifold is a torus, exhibit several novel features:
signed area phases relate the observables assigned to homotopic loops, and
their commutators describe loop intersections, with properties that are not yet
fully understood. We describe progress in our study of this bracket, which can
be interpreted as a q-deformed Goldman bracket, and provide a geometrical
interpretation in terms of a quantum version of Pick's formula for the area of
a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved
figures and extra figures. To appear GER
Comparative Quantizations of (2+1)-Dimensional Gravity
We compare three approaches to the quantization of (2+1)-dimensional gravity
with a negative cosmological constant: reduced phase space quantization with
the York time slicing, quantization of the algebra of holonomies, and
quantization of the space of classical solutions. The relationships among these
quantum theories allow us to define and interpret time-dependent operators in
the ``frozen time'' holonomy formulation.Comment: 24 pages, LaTeX, no figure
Distribution and Diversity of Archaeal and Bacterial Ammonia Oxidizers in Salt Marsh Sediments
Diversity and abundance of ammonia-oxidizing Betaproteobacteria (ÎČ-AOB) and archaea (AOA) were investigated in a New England salt marsh at sites dominated by short or tall Spartina alterniflora (SAS and SAT sites, respectively) or Spartina patens (SP site). AOA amoA gene richness was higher than ÎČ-AOB amoA richness at SAT and SP, but AOA and ÎČ-AOB richness were similar at SAS. ÎČ-AOB amoA clone libraries were composed exclusively of Nitrosospira-like amoA genes. AOA amoA genes at SAT and SP were equally distributed between the water column/sediment and soil/sediment clades, while AOA amoA sequences at SAS were primarily affiliated with the water column/sediment clade. At all three site types, AOA were always more abundant than ÎČ-AOB based on quantitative PCR of amoA genes. At some sites, we detected 109 AOA amoA gene copies g of sedimentâ1. Ratios of AOA to ÎČ-AOB varied over 2 orders of magnitude among sites and sampling dates. Nevertheless, abundances of AOA and ÎČ-AOB amoA genes were highly correlated. Abundance of 16S rRNA genes affiliated with Nitrosopumilus maritimus, Crenarchaeota group I.1b, and pSL12 were positively correlated with AOA amoA abundance, but ratios of amoA to 16S rRNA genes varied among sites. We also observed a significant effect of pH on AOA abundance and a significant salinity effect on both AOA and ÎČ-ÎÎÎ abundance. Our results expand the distribution of AOA to salt marshes, and the high numbers of AOA at some sites suggest that salt marsh sediments serve as an important habitat for AOA
Global constants in (2+1)--dimensional gravity
The extended conformal algebra (so)(2,3) of global, quantum, constants of
motion in 2+1 dimensional gravity with topology R x T^2 and negative
cosmological constant is reviewed. It is shown that the 10 global constants
form a complete set by expressing them in terms of two commuting spinors and
the Dirac gamma matrices. The spinor components are the globally constant
holonomy parameters, and their respective spinor norms are their quantum
commutators.Comment: 14 pages, to appear in Classical and Quantum Gravity, Spacetime
Safari: Essays in Honor of Vincent Moncrief on the Classical Physics of
Strong Gravitational Field
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
Three Numerical Puzzles and the Top Quark's Chiral Weak-Moment
Versus the standard model's t --> W b decay helicity amplitudes, three
numerical puzzles occur at the 0.1 % level when one considers the amplitudes in
the case of an additional (f_M + f_E) coupling of relative strength 53 GeV. The
puzzles are theoretical ones which involve the t --> W b decay helicity
amplitudes in the two cases, the relative strength of this additional coupling,
and the observed masses of these three particles. A deeper analytic realization
is obtained for two of them. Equivalent realizations are given for the
remaining one. An empirical consequence of these analytic realizations is that
it is important to search for effects of a large chiral weak-moment of the
top-quark, the effective mass-scale is about 53 GeV. A full theoretical
resolution would include relating the origin of such a chiral weak-moment and
the mass generation of the top-quark, the W-boson, and probably the b-quark.Comment: 18 pages, 1 postscript table (revised to better explain notation,
model #1, add a little material...
Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions
Two canonical formulations of the Einstein gravity in 2+1 dimensions, namely,
the ADM formalism and the Chern-Simons gravity, are investigated in the case of
nonvanishing cosmological constant. General arguments for reducing phase spaces
of the two formalisms are given when spatial hypersurface is compact. In
particular when the space has the topology of a sphere or a torus
, the spacetimes constructed from these two formulations can be
identified and the classical equivalence between the ADM and the CSG is shown.
Moreover in the case the relations between their phase spaces, and
therefore between their quantizations, are given in almost the same form as
that in the case when the cosmological constant vanishes. There are, however,
some modifications, the most remarkable one of which is that the phase space of
the CSG is in 1 to 2 correspondence with the one of the ADM when the
cosmological constant is negative.Comment: 37pages Latex (6 figures not included
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