8,469 research outputs found
Graphical representation of covariant-contravariant modal formulae
Covariant-contravariant simulation is a combination of standard (covariant)
simulation, its contravariant counterpart and bisimulation. We have previously
studied its logical characterization by means of the covariant-contravariant
modal logic. Moreover, we have investigated the relationships between this
model and that of modal transition systems, where two kinds of transitions (the
so-called may and must transitions) were combined in order to obtain a simple
framework to express a notion of refinement over state-transition models. In a
classic paper, Boudol and Larsen established a precise connection between the
graphical approach, by means of modal transition systems, and the logical
approach, based on Hennessy-Milner logic without negation, to system
specification. They obtained a (graphical) representation theorem proving that
a formula can be represented by a term if, and only if, it is consistent and
prime. We show in this paper that the formulae from the covariant-contravariant
modal logic that admit a "graphical" representation by means of processes,
modulo the covariant-contravariant simulation preorder, are also the consistent
and prime ones. In order to obtain the desired graphical representation result,
we first restrict ourselves to the case of covariant-contravariant systems
without bivariant actions. Bivariant actions can be incorporated later by means
of an encoding that splits each bivariant action into its covariant and its
contravariant parts.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407
Covariant Formulation of the Invariant Measure for the Mixmaster Dynamics
We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing
the covariant nature of its chaotic behavior with respect to any choice of time
variable. We construct the appropriate invariant measure for the system (which
relies on the existence of an ``energy-like'' constant of motion) without
fixing the time gauge, i.e. the corresponding lapse function. The key point in
our analysis consists of introducing generic Misner-Chitr\'e-like variables
containing an arbitrary function, whose specification allows one to set up the
same dynamical scheme in any time gauge.Comment: 11 pages, 1 figur
Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedure
The standard covariant differentiation procedure for fields in vector bundles
is generalised so as to be applicable to fields in general nonaffine bundles in
which the fibres may have an arbitrary nonlinear structure. In addition to the
usual requirement that the base space should be flat or endowed with its own
linear connection, and that there should be an ordinary gauge connection on the
bundle, it is necessary to require also that there should be an intrinsic,
bundle-group invariant connection on the fibre space. The procedure is based on
the use of an appropriate primary-field (i.e. section) independent connector
that is constructed in terms of the natural fibre-tangent-vector realisation of
the gauge connection. The application to gauged harmonic mappings will be
described in a following article.Comment: 17 page Latex file with some minor misprint corrections and added
color for article originally published in black and whit
On the concept of Bell's local causality in local classical and quantum theory
The aim of this paper is to give a sharp definition of Bell's notion of local
causality. To this end, first we unfold a framework, called local physical
theory, integrating probabilistic and spatiotemporal concepts. Formulating
local causality within this framework and classifying local physical theories
by whether they obey local primitive causality --- a property rendering the
dynamics of the theory causal, we then investigate what is needed for a local
physical theory, with or without local primitive causality, to be locally
causal. Finally, comparing Bell's local causality with the Common Cause
Principles and relating both to the Bell inequalities we find a nice
parallelism: Bell inequalities cannot be derived neither from local causality
nor from a common cause unless the local physical theory is classical or the
common cause is commuting, respectively.Comment: 24 pages, 5 figure
PROCRUSTES: A computer algebra package for post-Newtonian calculations in General Relativity
We report on a package of routines for the computer algebra system Maple
which supports the explicit determination of the geometric quantities, field
equations, equations of motion, and conserved quantities of General Relativity
in the post-Newtonian approximation. The package structure is modular and
allows for an easy modification by the user. The set of routines can be used to
verify hand calculations or to generate the input for further numerical
investigations.Comment: 20 pages, 3 figures. The latest version of the package can be
obtained from http://www.thp.uni-koeln.de/~dp/procrustes.htm
Relativistic state reduction dynamics
A mechanism describing state reduction dynamics in relativistic quantum field
theory is outlined. The mechanism involves nonlinear stochastic modifications
to the standard description of unitary state evolution and the introduction of
a relativistic field in which a quantized degree of freedom is associated to
each point in spacetime. The purpose of this field is to mediate in the
interaction between classical stochastic influences and conventional quantum
fields. The equations of motion are Lorentz covariant, frame independent, and
do not result in divergent behavior. It is shown that the mathematical
framework permits the specification of unambiguous local properties providing a
connection between the model and evidence of real world phenomena. The collapse
process is demonstrated for an idealized example.Comment: 20 pages, 2 figures, replacement with minor correction
Electromagnetic Deflection of Spinning Particles
We show that it is possible to obtain self-consistent and physically
acceptable relativistic classical equations of motion for a point-like
spin-half particle possessing an electric charge and a magnetic dipole moment,
directly from a manifestly covariant Lagrangian, if the classical degrees of
freedom are appropriately chosen. It is shown that the equations obtained
encompass the well-tested Lorentz force and Thomas--Bargmann--Michel--Telegdi
spin equations, as well as providing a definite specification of the classical
_magnetic_dipole_ force_, whose exact form has been the subject of recent
debate. Radiation reaction---the force and torque on an accelerated particle
due to its self-interaction---is neglected at this stage.Comment: 18 pp. (latex, uses revtex 3), UM-P-92/9
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