14,117 research outputs found
Gurses' Type (b) Transformations are Neighborhood-Isometries
Following an idea close to one given by C. G. Torre (private communication),
we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses
type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or,
equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and
I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric,
i.e., every point x in M has a corresponding diffeomorphism phi of a
neighborhood V of x onto a generally different neighborhood W of x such that
phi*(h|W) = g|V.Comment: 10 pages, LATEX, FJE-93-00
EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited
In 1930 Einstein argued against consistency of the time-energy uncertainty
relation by discussing a thought experiment involving a measurement of mass of
the box which emitted a photon. Bohr seemingly triumphed over Einstein by
arguing that the Einstein's own general theory of relativity saves the
consistency of quantum mechanics. We revisit this thought experiment from a
modern point of view at a level suitable for undergraduate readership and find
that neither Einstein nor Bohr was right. Instead, this thought experiment
should be thought of as an early example of a system demonstrating nonlocal
"EPR" quantum correlations, five years before the famous
Einstein-Podolsky-Rosen paper.Comment: 11 pages, revised, accepted for publication in Eur. J. Phy
Classification of Generalized Symmetries for the Vacuum Einstein Equations
A generalized symmetry of a system of differential equations is an
infinitesimal transformation depending locally upon the fields and their
derivatives which carries solutions to solutions. We classify all generalized
symmetries of the vacuum Einstein equations in four spacetime dimensions. To
begin, we analyze symmetries that can be built from the metric, curvature, and
covariant derivatives of the curvature to any order; these are called natural
symmetries and are globally defined on any spacetime manifold. We next classify
first-order generalized symmetries, that is, symmetries that depend on the
metric and its first derivatives. Finally, using results from the
classification of natural symmetries, we reduce the classification of all
higher-order generalized symmetries to the first-order case. In each case we
find that the generalized symmetries are infinitesimal generalized
diffeomorphisms and constant metric scalings. There are no non-trivial
conservation laws associated with these symmetries. A novel feature of our
analysis is the use of a fundamental set of spinorial coordinates on the
infinite jet space of Ricci-flat metrics, which are derived from Penrose's
``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te
Molecular evidence of incipient speciation within Anopheles gambiae s.s. in West Africa
We karyotyped and identified by polymerase chain reaction restriction fragment length polymorphism (PCR-RFLP) analysis Anopheles gambiae s.s. samples collected in several African countries. The data show the existence of two non-panmictic molecular forms, named S and M, whose distribution extended from forest to savannahs, Mosquitoes of the S and M forms are homosequential standard for chromosome-2 inversions in forest areas. In dry savannahs, S is characterized mainly by inversion polymorphisms typical of Savanna and Bamako chromosomal forms, while M shows chromosome-2 arrangements typical of Mopti and/or Savanna and/or Bissau, depending on its geographical origin. Chromosome-2 inversions therefore seem to be involved in ecotypic adaptation rather than in mate-recognition systems. Strong support for the reproductive isolation of S and M in Ivory Coast comes from the observation that the kdr allele is found at high frequencies in S specimens and not at all in chromosomal identical M specimens. However, the kdr allele does not segregate with molecular forms in Benin
On the Coherent State Path Integral for Linear Systems
We present a computation of the coherent state path integral for a generic
linear system using ``functional methods'' (as opposed to discrete time
approaches). The Gaussian phase space path integral is formally given by a
determinant built from a first-order differential operator with coherent state
boundary conditions. We show how this determinant can be expressed in terms of
the symplectic transformation generated by the (in general, time-dependent)
quadratic Hamiltonian for the system. We briefly discuss the conditions under
which the coherent state path integral for a linear system actually exists. A
necessary -- but not sufficient -- condition for existence of the path integral
is that the symplectic transformation generated by the Hamiltonian is
(unitarily) implementable on the Fock space for the system.Comment: 15 pages, plain Te
Classical and quantum time dependent solutions in string theory
Using the ontological interpretation of quantum mechanics in a particular
sense, we obtain the classical behaviour of the scale factor and two scalar
fields, derived from a string effective action for the FRW time dependent
model. Besides, the Wheeler-DeWitt equation is solved exactly. We speculate
that the same procedure could also be applied to S-branes.Comment: 11 pages, To appear in Int. J. Mod. Phys.
Gauge-invariant Hamiltonian dynamics of cylindrical gravitational waves
The model of cylindrical gravitational waves is employed to work out and
check a recent proposal in Ref. [11] how a diffeomorphism-invariant Hamiltonian
dynamics is to be constructed. The starting point is the action by Ashtekar and
Pierri because it contains the boundary term that makes it differentiable for
non-trivial variations at infinity. With the help of parametrization at
infinity, the notion of gauge transformation is clearly separated from that of
asymptotic symmetry. The symplectic geometry of asymptotic symmetries and
asymptotic time is described and the role of the asymptotic structures in
defining a zero-motion frame for the Hamiltonian dynamics of Dirac observables
is explained. Complete sets of Dirac observables associated with the asymptotic
fields are found and the action of the asymptotic symmetries on them is
calculated. The construction of the corresponding quantum theory is sketched:
the Fock space, operators of asymptotic fields, the Hamiltonian and the
scattering matrix are determined.Comment: 16 pages, 1 figur
The isolation of gravitational instantons: Flat tori V flat R^4
The role of topology in the perturbative solution of the Euclidean Einstein
equations about flat instantons is examined.Comment: 15 pages, ICN-UNAM 94-1
- …