3,474 research outputs found
Base-controlled mechanical systems and geometric phases
In this paper, we carry a detailed study of mechanical systems with
configuration space for which the base variables
are being controlled. The overall system's motion is considered to be induced
from the base one due to the presence of general non-holonomic constraints. It
is shown that the solution can be factorized into dynamical and geometrical
parts. Moreover, under favorable kinematical circumstances, the dynamical part
admits a further factorization since it can be reconstructed from an
intermediate (body) momentum solution, yielding a reconstruction phase formula.
Finally, we apply this results to the study of concrete mechanical systems.Comment: 44 pages, 1 figur
Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
This paper contains three results about generating functions for
Lie-theoretic integration of Poisson brackets and their relation to
quantization. In the first, we show how to construct a generating function
associated to the germ of any local symplectic groupoid and we provide an
explicit (smooth, non-formal) universal formula for integrating any
Poisson structure on a coordinate space. The second result involves the
relation to semiclassical quantization. We show that the formal Taylor
expansion of around yields an extract of Kontsevich's star
product formula based on tree-graphs, recovering the formal family introduced
by Cattaneo, Dherin and Felder in [6]. The third result involves the relation
to semiclassical aspects of the Poisson Sigma model. We show that can
be obtained by non-perturbative functional methods, evaluating a certain
functional on families of solutions of a PDE on a disk, for which we show
existence and classification.Comment: 53 pages, 2 figure
Differentiability of correlations in Realistic Quantum Mechanics
We prove a version of Bell's Theorem in which the Locality assumption is
weakened. We start by assuming theoretical quantum mechanics and weak forms of
relativistic causality and of realism (essentially the fact that observable
values are well defined independently of whether or not they are measured).
Under these hypotheses, we show that only one of the correlation functions that
can be formulated in the framework of the usual Bell theorem is unknown. We
prove that this unknown function must be differentiable at certain angular
configuration points that include the origin. We also prove that, if this
correlation is assumed to be twice differentiable at the origin, then we arrive
at a version of Bell's theorem. On the one hand, we are showing that any
realistic theory of quantum mechanics which incorporates the kinematic aspects
of relativity must lead to this type of \emph{rough} correlation function that
is once but not twice differentiable. On the other hand, this study brings us a
single degree of differentiability away from a relativistic von Neumann no
hidden variables theorem.Comment: Final version, published in JM
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