682 research outputs found
Loop quantization from a lattice gauge theory perspective
We present an interpretation of loop quantization in the framework of lattice
gauge theory. Within this context the lack of appropriate notions of effective
theories and renormalization group flow exhibit loop quantization as an
incomplete framework. This interpretation includes a construction of embedded
spin foam models which does not rely on the choice of any auxiliary structure
(e.g. triangulation) and has the following straightforward consequences: (1)
The values of the coupling constants need to be those of an UV-attractive fixed
point (2) The kinematics of canonical loop quantization and embedded spin foam
models are compatible (3) The weights assigned to embedded spin foams are
independent of the 2-polyhedron used to regularize the path integral, (4) An area spectrum with edge contributions proportional to is not compatible with embedded spin foam models and/or
canonical loop quantizationComment: 11 pages, no figures; completely rewritte
Gauge from holography and holographic gravitational observables
In a spacetime divided into two regions and by a hypersurface
, a perturbation of the field in is coupled to perturbations in
by means of the holographic imprint that it leaves on . The
linearized gluing field equation constrains perturbations on the two sides of a
dividing hypersurface, and this linear operator may have a nontrivial null
space. A nontrivial perturbation of the field leaving a holographic imprint on
a dividing hypersurface which does not affect perturbations on the other side
should be considered physically irrelevant. This consideration, together with a
locality requirement, leads to the notion of gauge equivalence in Lagrangian
field theory over confined spacetime domains.
Physical observables in a spacetime domain can be calculated integrating
(possibly non local) gauge invariant conserved currents on hypersurfaces such
that . The set of observables of this type
is sufficient to distinguish gauge inequivalent solutions. The integral of a
conserved current on a hypersurface is sensitive only to its homology class
, and if is homeomorphic to a four ball the homology class is
determined by its boundary . We will see that a result of
Anderson and Torre implies that for a class of theories including vacuum
General Relativity all local observables are holographic in the sense that they
can be written as integrals of over the two dimensional surface . However,
non holographic observables are needed to distinguish between gauge
inequivalent solutions
Local gauge theory and coarse graining
Within the discrete gauge theory which is the basis of spin foam models, the
problem of macroscopically faithful coarse graining is studied. Macroscopic
data is identified; it contains the holonomy evaluation along a discrete set of
loops and the homotopy classes of certain maps. When two configurations share
this data they are related by a local deformation. The interpretation is that
such configurations differ by "microscopic details". In many cases the homotopy
type of the relevant maps is trivial for every connection; two important cases
in which the homotopy data is composed by a set of integer numbers are: (i) a
two dimensional base manifold and structure group U(1), (ii) a four dimensional
base manifold and structure group SU(2). These cases are relevant for spin foam
models of two dimensional gravity and four dimensional gravity respectively.
This result suggests that if spin foam models for two-dimensional and
four-dimensional gravity are modified to include all the relevant macroscopic
degrees of freedom -the complete collection of macroscopic variables necessary
to ensure faithful coarse graining-, then they could provide appropriate
effective theories at a given scale.Comment: Based on talk given at Loops 11-Madri
Curvature function and coarse graining
A classic theorem in the theory of connections on principal fiber bundles
states that the evaluation of all holonomy functions gives enough information
to characterize the bundle structure (among those sharing the same structure
group and base manifold) and the connection up to a bundle equivalence map.
This result and other important properties of holonomy functions has encouraged
their use as the primary ingredient for the construction of families of quantum
gauge theories. However, in these applications often the set of holonomy
functions used is a discrete proper subset of the set of holonomy functions
needed for the characterization theorem to hold. We show that the evaluation of
a discrete set of holonomy functions does not characterize the bundle and does
not constrain the connection modulo gauge appropriately.
We exhibit a discrete set of functions of the connection and prove that in
the abelian case their evaluation characterizes the bundle structure (up to
equivalence), and constrains the connection modulo gauge up to "local details"
ignored when working at a given scale. The main ingredient is the Lie algebra
valued curvature function defined below. It covers the holonomy
function in the sense that .Comment: 34 page
La convección y su tratamiento en los modelos de predicción numérica del tiempo
Los modelos de predicción numérica del tiempo han constituido uno de los avances más importantes de la meteorología, tanto de la investigación meteorológica como de la llamada meteorología operativa. Las predicciones del tiempo han mejorado como resultado de la constante mejora de los modelos numéricos. Como no es posible simular en laboratorio los procesos atmosféricos cualquier estudio sobre alguno de estos procesos debe hacerse en el marco de un modelo numérico que aporte el comportamiento general de la atmósfera. La convección atmosférica es uno de los procesos más importantes de los que regulan la redistribución energética en la atmósfera y uno de los temas más importantes en la investigación meteorológica. Este artículo realiza una revisión general y simplificada de los distintos esquemas que parametrizan los procesos convectivos dentro de los modelos numéricos. Tras una breve descripción de diferentes esquemas mostraremos los resultados de aplicar algunos de ellos a una situación de lluvias fuertes convectivas en España
Homotopy data as part of the lattice field: A first study
Fields exhibit a variety of topological properties, like different
topological charges, when field space in the continuum is composed by more than
one topological sector. Lattice treatments usually encounter difficulties
describing those properties. In this work, we show that by augmenting the usual
lattice fields to include extra variables describing local topological
information (more precisely, regarding homotopy), the topology of the space of
fields in the continuum is faithfully reproduced in the lattice. We apply this
extended lattice formulation to some simple models with non-trivial topological
charges, and we study their properties both analytically and via Monte Carlo
simulations.Comment: We added some references and a section where we make contact between
the extended lattice formalism and the usual lattice variables augmented with
an integer lattice field in the dual lattice. We made some corrections,
including changing the title and the abstract, after referee's corrections
and critique
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