19,752 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
Optimal Capacity of the Blume-Emery-Griffiths perceptron
A Blume-Emery-Griffiths perceptron model is introduced and its optimal
capacity is calculated within the replica-symmetric Gardner approach, as a
function of the pattern activity and the imbedding stability parameter. The
stability of the replica-symmetric approximation is studied via the analogue of
the Almeida-Thouless line. A comparison is made with other three-state
perceptrons.Comment: 10 pages, 8 figure
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
High-dimensional neutrino masses
For Majorana neutrino masses the lowest dimensional operator possible is the
Weinberg operator at . Here we discuss the possibility that neutrino
masses originate from higher dimensional operators. Specifically, we consider
all tree-level decompositions of the , and neutrino mass
operators. With renormalizable interactions only, we find 18 topologies and 66
diagrams for , and 92 topologies plus 504 diagrams at the level. At
there are already 576 topologies and 4199 diagrams. However, among all
these there are only very few genuine neutrino mass models: At we
find only (2,2,2) genuine diagrams and a total of (2,2,6) models. Here, a model
is considered genuine at level if it automatically forbids lower order
neutrino masses {\em without} the use of additional symmetries. We also briefly
discuss how neutrino masses and angles can be easily fitted in these
high-dimensional models.Comment: Coincides with published version in JHE
The single scattering phase functions of Jupiter's clouds
The determination of the single scattering phase functions of Jupiter's clouds and a thin upper haze by Tomasko et al. was refined and extended to seven latitudes in blue and red light. The phase function is well-constrained by the Pioneer 10 and 11 photometric data sets. Multiple scattering models were computed to match the limb darkening at each latitude at up to 15 phase angles from 12 deg to 151 deg. Ground-based observations were used for absolute calibration and to extend the data to lower phase angles. The phase functions were parameterized using the double Henyey-Greenstein function. The three Henyey-Greenstein parameters and the single scattering albedo were determined using a non-linear least squares method for the haze and the clouds below. The phase functions derived for the northen zone and belt are remarkably similar to the phase functions of the corresponding regions in the south, with most of the differences in brightness of the northern and southern features resulting from minor differences in single scattering albedo. Analysis of the Equatorial Region is complicated by the presence of numerous small features, but the phase function required is generally similar to that seen in the more homogeneous regions. Details of the phase functions of the haze and clouds are presented, and the differences between the cloud phase functions at low and high latitudes in red and blue light are discussed
Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation
By using conformal Killing-Yano tensors, and their generalisations, we obtain
scalar potentials for both the source-free Maxwell and massless Dirac
equations. For each of these equations we construct, from conformal
Killing-Yano tensors, symmetry operators that map any solution to another.Comment: 35 pages, plain Te
Casimir interaction at liquid nitrogen temperature: Comparison between experiment and theory
We have measured the normalized gradient of the Casimir force between
Au-coated surfaces of the sphere and the plate and equivalent Casimir pressure
between two parallel Au plates at T=77K. These measurements have been performed
by means of dynamic force microscope adapted for operating at low temperatures
in the frequency shift technique. It was shown that the measurement results at
T=77K are in a very good agreement with those at T=300K and with computations
at T=77K using both theoretical approaches to the thermal Casimir force
proposed in the literature. No thermal effect in the Casimir pressure was
observed in the limit of experimental errors with the increase of temperature
from T=77K to T=300K. Taking this into account, we have discussed the possible
role of patch potentials in the comparison between measured and calculated
Casimir pressures.Comment: 18 pages, 8 figures, to appear in Phys. Rev.
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