504 research outputs found
The numerical study of the solution of the model
We present a numerical study of the nonlinear system of equations
of motion. The solution is obtained iteratively, starting from a precise
point-sequence of the appropriate Banach space, for small values of the
coupling constant. The numerical results are in perfect agreement with the main
theoretical results established in a series of previous publications.Comment: arxiv version is already officia
Quantum Gowdy Model: Schrodinger Representation with Unitary Dynamics
The linearly polarized Gowdy model is paradigmatic for studying
technical and conceptual issues in the quest for a quantum theory of gravity
since, after a suitable and almost complete gauge fixing, it becomes an exactly
soluble midisuperspace model. Recently, a new quantization of the model,
possessing desired features such as a unitary implementation of the gauge group
and of the time evolution, has been put forward and proven to be essentially
unique. An appropriate setting for making contact with other approaches to
canonical quantum gravity is provided by the Schr\"odinger representation,
where states are functionals on the configuration space of the theory. Here we
construct this functional description, analyze the time evolution in this
context and show that it is also unitary when restricted to physical states,
i.e. states which are solutions to the remaining constraint of the theory.Comment: 21 pages, version accepted for publication in Physical Review
The embedding structure and the shift operator of the U(1) lattice current algebra
The structure of block-spin embeddings of the U(1) lattice current algebra is
described. For an odd number of lattice sites, the inner realizations of the
shift automorphism areclassified. We present a particular inner shift operator
which admits a factorization involving quantum dilogarithms analogous to the
results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected;
version to appear in Lett.Math.Phy
Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case
We construct quantum operators solving the quantum versions of the
Sturm-Liouville equation and the resolvent equation, and show the existence of
conserved currents. The construction depends on the following input data: the
basic quantum field and the regularization .Comment: minor correction
On the support of the Ashtekar-Lewandowski measure
We show that the Ashtekar-Isham extension of the classical configuration
space of Yang-Mills theories (i.e. the moduli space of connections) is
(topologically and measure-theoretically) the projective limit of a family of
finite dimensional spaces associated with arbitrary finite lattices. These
results are then used to prove that the classical configuration space is
contained in a zero measure subset of this extension with respect to the
diffeomorphism invariant Ashtekar-Lewandowski measure.
Much as in scalar field theory, this implies that states in the quantum
theory associated with this measure can be realized as functions on the
``extended" configuration space.Comment: 22 pages, Tex, Preprint CGPG-94/3-
Algebraic Quantum Theory on Manifolds: A Haag-Kastler Setting for Quantum Geometry
Motivated by the invariance of current representations of quantum gravity
under diffeomorphisms much more general than isometries, the Haag-Kastler
setting is extended to manifolds without metric background structure. First,
the causal structure on a differentiable manifold M of arbitrary dimension
(d+1>2) can be defined in purely topological terms, via cones (C-causality).
Then, the general structure of a net of C*-algebras on a manifold M and its
causal properties required for an algebraic quantum field theory can be
described as an extension of the Haag-Kastler axiomatic framework.
An important application is given with quantum geometry on a spatial slice
within the causally exterior region of a topological horizon H, resulting in a
net of Weyl algebras for states with an infinite number of intersection points
of edges and transversal (d-1)-faces within any neighbourhood of the spatial
boundary S^2.Comment: 15 pages, Latex; v2: several corrections, in particular in def. 1 and
in sec.
Two and Three Loops Beta Function of Non Commutative Theory
The simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is asymptotically
safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this
result up to three loops. If this remains true at any loop, it should allow a
full non perturbative construction of this model.Comment: 24 pages, 7 figure
Monte Carlo Simulation Calculation of Critical Coupling Constant for Continuum \phi^4_2
We perform a Monte Carlo simulation calculation of the critical coupling
constant for the continuum {\lambda \over 4} \phi^4_2 theory. The critical
coupling constant we obtain is [{\lambda \over \mu^2}]_crit=10.24(3).Comment: 11 pages, 4 figures, LaTe
Ontology-based data access with databases: a short course
Ontology-based data access (OBDA) is regarded as a key ingredient of the new generation of information systems. In the OBDA paradigm, an ontology defines a high-level global schema of (already existing) data sources and provides a vocabulary for user queries. An OBDA system rewrites such queries and ontologies into the vocabulary of the data sources and then delegates the actual query evaluation to a suitable query answering system such as a relational database management system or a datalog engine. In this chapter, we mainly focus on OBDA with the ontology language OWL 2QL, one of the three profiles of the W3C standard Web Ontology Language OWL 2, and relational databases, although other possible languages will also be discussed. We consider different types of conjunctive query rewriting and their succinctness, different architectures of OBDA systems, and give an overview of the OBDA system Ontop
Universality in Blow-Up for Nonlinear Heat Equations
We consider the classical problem of the blowing-up of solutions of the
nonlinear heat equation. We show that there exist infinitely many profiles
around the blow-up point, and for each integer , we construct a set of
codimension in the space of initial data giving rise to solutions that
blow-up according to the given profile.Comment: 38 page
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