35,345 research outputs found
Semiclassical Approach to Finite-N Matrix Models
We reformulate the zero-dimensional hermitean one-matrix model as a
(nonlocal) collective field theory, for finite~. The Jacobian arising by
changing variables from matrix eigenvalues to their density distribution is
treated {\it exactly\/}. The semiclassical loop expansion turns out {\it not\/}
to coincide with the (topological) ~expansion, because the
classical background has a non-trivial -dependence. We derive a simple
integral equation for the classical eigenvalue density, which displays strong
non-perturbative behavior around . This leads to IR singularities
in the large- expansion, but UV divergencies appear as well, despite
remarkable cancellations among the Feynman diagrams. We evaluate the free
energy at the two-loop level and discuss its regularization. A simple example
serves to illustrate the problems and admits explicit comparison with
orthogonal polynomial results.Comment: 27 pages / 3 figures (ps file fixed
Asymptotic flexibility of globally hyperbolic manifolds
In this short note, a question of patching together globally hyperbolic
manifolds is adressed which appeared in the context of the construction of
Hadamard states.Comment: 2 pages, submitted to 'Mathematische Zeitschrift
Degeneracies and scaling relations in general power-law models for gravitational lenses
The time delay in gravitational lenses can be used to derive the Hubble
constant in a relatively simple way. The results of this method are less
dependent on astrophysical assumptions than in many other methods. The most
important uncertainty is related to the mass model used. We discuss a family of
models with a separable radial power-law and an arbitrary angular dependence
for the potential psi = r^beta * F(theta). Isothermal potentials are a special
case of these models with beta=1. An additional external shear is used to take
into account perturbations from other galaxies. Using a simple linear formalism
for quadruple lenses, we can derive H0 as a function of the observables and the
shear. If the latter is fixed, the result depends on the assumed power-law
exponent according to H0 proportional to (2-beta)/beta. The effect of external
shear is quantified by introducing a `critical shear' gamma_c as a measure for
the amount of shear that changes the result significantly. The analysis shows,
that in the general case H0 and gamma_c do not depend on the position of the
lens galaxy. We discuss these results and compare with numerical models for a
number of real lens systems.Comment: accepted for publication in MNRAS, 10 pages, 4 figures (eps
included), uses mn2e.cls, amsmath.sty, times.st
Ln(3) and Black Hole Entropy
We review an idea that uses details of the quasinormal mode spectrum of a
black hole to obtain the Bekenstein-Hawking entropy of in Loop Quantum
Gravity. We further comment on a recent proposal concerning the quasinormal
mode spectrum of rotating black holes. We conclude by remarking on a recent
proposal to include supersymmetry.Comment: Contribution to the Proceedings of the 3rd International Symposium on
Quantum Theory and Symmetries, Cincinnati, September 2003, added references
to the numerical investigations of Kerr quasinormal modes by Berti et. a
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