8,602 research outputs found
Penrose Limits and Spacetime Singularities
We give a covariant characterisation of the Penrose plane wave limit: the
plane wave profile matrix is the restriction of the null geodesic
deviation matrix (curvature tensor) of the original spacetime metric to the
null geodesic, evaluated in a comoving frame. We also consider the Penrose
limits of spacetime singularities and show that for a large class of black
hole, cosmological and null singularities (of Szekeres-Iyer ``power-law
type''), including those of the FRW and Schwarzschild metrics, the result is a
singular homogeneous plane wave with profile , the scale
invariance of the latter reflecting the power-law behaviour of the
singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction
Fermi Coordinates and Penrose Limits
We propose a formulation of the Penrose plane wave limit in terms of null
Fermi coordinates. This provides a physically intuitive (Fermi coordinates are
direct measures of geodesic distance in space-time) and manifestly covariant
description of the expansion around the plane wave metric in terms of
components of the curvature tensor of the original metric, and generalises the
covariant description of the lowest order Penrose limit metric itself, obtained
in hep-th/0312029. We describe in some detail the construction of null Fermi
coordinates and the corresponding expansion of the metric, and then study
various aspects of the higher order corrections to the Penrose limit. In
particular, we observe that in general the first-order corrected metric is such
that it admits a light-cone gauge description in string theory. We also
establish a formal analogue of the Weyl tensor peeling theorem for the Penrose
limit expansion in any dimension, and we give a simple derivation of the
leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page
The Supply of Quality in Child Care Centers
We use data from a sample of day care centers to estimate the relationships between cost and the quality of the child care service provided, and between revenue and quality. We use a measure of child care quality derived from an instrument designed by developmental psychologists. This measure of quality has been found to be positively associated with child development. Taking the estimated cost-quality and revenue-quality relationships as given, we then estimate the objective functions of the firms and compute the supply function for quality. The results indicate that (1) the estimated cost function is inconsistent with the implications of cost-minimization; (2) for-profit firms operate at a positive level of marginal cost, but non-profit firms operate at zero or negative marginal cost; (3) revenue is positively but weakly associated with quality; and (4) the supply of quality is inelastic, with point estimates of the supply elasticity of .04-.05 for both for-profit and non-profit firms. Implications of the results for child care policy are discussed.
Symmetries and Observables for BF-theories in Superspace
The supersymmetric version of a topological quantum field theory describing
flat connections, the super BF-theory, is studied in the superspace formalism.
A set of observables related to topological invariants is derived from the
curvature of the superspace. Analogously to the non-supersymmetric versions,
the theory exhibits a vector-like supersymmetry. The role of the vector
supersymmetry and an additional new symmetry of the action in the construction
of observables is explained.Comment: 11 pages, LaTe
The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes
This work considers the way that quantum loop effects modify the propagation
of light in curved space. The calculation of the refractive index for scalar
QED is reviewed and then extended for the first time to QED with spinor
particles in the loop. It is shown how, in both cases, the low frequency phase
velocity can be greater than c, as found originally by Drummond and Hathrell,
but causality is respected in the sense that retarded Green functions vanish
outside the lightcone. A "phenomenology" of the refractive index is then
presented for black holes, FRW universes and gravitational waves. In some
cases, some of the polarization states propagate with a refractive index having
a negative imaginary part indicating a potential breakdown of the optical
theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph
Computer program compatible with a laser nephelometer
The laser nephelometer data system was updated to provide magnetic tape recording of data, and real time or near real time processing of data to provide particle size distribution and liquid water content. Digital circuits were provided to interface the laser nephelometer to a Data General Nova 1200 minicomputer. Communications are via a teletypewriter. A dual Linc Magnetic Tape System is used for program storage and data recording. Operational programs utilize the Data General Real-Time Operating System (RTOS) and the ERT AIRMAP Real-Time Operating System (ARTS). The programs provide for acquiring data from the laser nephelometer, acquiring data from auxiliary sources, keeping time, performing real time calculations, recording data and communicating with the teletypewriter
Topological Aspects of Gauge Fixing Yang-Mills Theory on S4
For an space-time manifold global aspects of gauge-fixing are
investigated using the relation to Topological Quantum Field Theory on the
gauge group. The partition function of this TQFT is shown to compute the
regularized Euler character of a suitably defined space of gauge
transformations. Topological properties of the space of solutions to a
covariant gauge conditon on the orbit of a particular instanton are found using
the isometry group of the base manifold. We obtain that the Euler
character of this space differs from that of an orbit in the topologically
trivial sector. This result implies that an orbit with Pontryagin number
\k=\pm1 in covariant gauges on contributes to physical correlation
functions with a different multiplicity factor due to the Gribov copies, than
an orbit in the trivial \k=0 sector. Similar topological arguments show that
there is no contribution from the topologically trivial sector to physical
correlation functions in gauges defined by a nondegenerate background
connection. We discuss possible physical implications of the global gauge
dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure
Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories
We review localization techniques for functional integrals which have
recently been used to perform calculations in and gain insight into the
structure of certain topological field theories and low-dimensional gauge
theories. These are the functional integral counterparts of the Mathai-Quillen
formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula
respectively. In each case, we first introduce the necessary mathematical
background (Euler classes of vector bundles, equivariant cohomology, topology
of Lie groups), and describe the finite dimensional integration formulae. We
then discuss some applications to path integrals and give an overview of the
relevant literature. The applications we deal with include supersymmetric
quantum mechanics, cohomological field theories, phase space path integrals,
and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of
Mathematical Physics Special Issue on Functional Integration (May 1995)
M-theory on a Time-dependent Plane-wave
We propose a matrix model on a homogeneous plane-wave background with 20
supersymmetries. This background is anti-Mach type and is equivalent to the
time-dependent background. We study supersymmetries in this theory and
calculate the superalgebra. The vacuum energy of the abelian part is also
calculated. In addition we find classical solutions such as graviton solution,
fuzzy sphere and hyperboloid.Comment: 19pages, no figures, LaTeX, JHEP3.cl
The Supply of Quality in Child Care Centers
We use data from a sample of child care centers to estimate the relationships between cost and child care quality, and between revenue and quality. We use a measure of child care quality, designed by developmental psychologists, that is positively associated with child development. Taking the estimated cost-quality and revenue-quality relationships as given, we estimate the objective functions of firms and compute the quality supply function. The results indicate that the supply of quality is moderately elastic with respect to price and the wages of child care center workers. Implications of the results for child care policy are discussed. © 2002 by the President and Fellows of Harvard College and the Massachusetts Institute of Technolo
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