6,939 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
Local continuity laws on the phase space of Einstein equations with sources
Local continuity equations involving background fields and variantions of the
fields, are obtained for a restricted class of solutions of the
Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the
concept of the adjoint of a differential operator. Such covariant conservation
laws are generated by means of decoupled equations and their adjoints in such a
way that the corresponding covariantly conserved currents possess some
gauge-invariant properties and are expressed in terms of Debye potentials.
These continuity laws lead to both a covariant description of bilinear forms on
the phase space and the existence of conserved quantities. Differences and
similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page
Embedded Implementation of a Kalman Filter for the Fusion of Automotive Inertial Sensors Using CARLA Simulator
The aim of this paper is to build a real-time Kalman filter that collects and fuses sensor data from vehicles to provide more accurate information of the car’s position and orientation. This research work uses the Carla simulator as the platform to simulate a real environment.ITESO, A. C
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
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.
On the Quantum Mechanics for One Photon
This paper revisits the quantum mechanics for one photon from the modern
viewpoint and by the geometrical method. Especially, besides the ordinary
(rectangular) momentum representation, we provide an explicit derivation for
the other two important representations, called the cylindrically symmetrical
representation and the spherically symmetrical representation, respectively.
These other two representations are relevant to some current photon experiments
in quantum optics. In addition, the latter is useful for us to extract the
information on the quantized black holes. The framework and approach presented
here are also applicable to other particles with arbitrary mass and spin, such
as the particle with spin 1/2.Comment: 15 pages, typos corrected, references added, corrections and
improvements made owing to the anonymous referee's responsible and helpful
remarks, accepted for publication in Journal of Mathematical Physics:
Geometrothermodynamics
We present the fundamentals of geometrothermodynamics, an approach to study
the properties of thermodynamic systems in terms of differential geometric
concepts. It is based, on the one hand, upon the well-known contact structure
of the thermodynamic phase space and, on the other hand, on the metric
structure of the space of thermodynamic equilibrium states. In order to make
these two structures compatible we introduce a Legendre invariant set of
metrics in the phase space, and demand that their pullback generates metrics on
the space of equilibrium states. We show that Weinhold's metric, which was
introduced {\it ad hoc}, is not contained within this invariant set. We propose
alternative metrics which allow us to redefine the concept of thermodynamic
length in an invariant manner and to study phase transitions in terms of
curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy
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