6,312 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
Category and Topological Complexity of the configuration space
The Lusternik-Schnirelmann category cat and topological complexity TC are
related homotopy invariants. The topological complexity TC has applications to
the robot motion planning problem. We calculate the Lusternik-Schnirelmann
category and topological complexity of the ordered configuration space of two
distinct points in the product and apply the results to
the planar and spatial motion of two rigid bodies in and
respectively.Comment: 10 pages, 1 figure. Final version. To appear in Bulletin of the
Australian Mathematical Societ
Quantum Structure of Geometry: Loopy and fuzzy?
In any attempt to build a quantum theory of gravity, a central issue is to
unravel the structure of space-time at the smallest scale. Of particular
relevance is the possible definition of coordinate functions within the theory
and the study of their algebraic properties, such as non-commutativity. Here we
approach this issue from the perspective of loop quantum gravity and the
picture of quantum geometry that the formalism offers. In particular, as we
argue here, this emerging picture has two main elements: i) The nature of the
quantum geometry at Planck scale is one-dimensional, polymeric with quantized
geometrical quantities and; ii) Appropriately defined operators corresponding
to coordinates by means of intrinsic, relational, constructions become
non-commuting. This particular feature of the operators, that operationally
localize points on space, gives rise to an emerging geometry that is also, in a
precise sense, fuzzy.Comment: 9 pages, no figure
A contracting circumbinary molecular ring with an inner cavity of about 140 AU around Ori 139-409
Sensitive and subarcsecond resolution ( 0.7\arcsec) CHOH(7
6) line and 890 m continuum observations made with the
Submillimeter Array (SMA) towards the hot molecular circumbinary ring
associated with the young multiple star Ori 139-409 are presented. The
CHOH(7 - 6) emission from the ring is well resolved at
this angular resolution revealing an inner cavity with a size of about 140 AU.
A LTE model of a Keplerian disk with an inner cavity of the same size confirms
the presence of this cavity. Additionally, this model suggests that the
circumbinary ring is contracting with a velocity of V 1.5 km
s toward the binary central compact circumstellar disks reported at a
wavelength of 7 mm. {\bf The inner central cavity seems to be formed by the
tidal effects of the young stars in the middle of the ring.} The ring appears
to be not a stationary object. Furthermore, the infall velocity we determine is
about a factor of 3 slower than the free-fall velocity corresponding to the
dynamical mass. This would correspond to a mass accretion rate of about
10 M/yr. We found that the dust emission associated with Ori
139-409 appears to be arising from the circumstellar disks with no strong
contribution from the molecular gas ring. A simple comparison with other
classical molecular dusty rings (e.g. GG Tau, UZ Tau, and UY Aur) suggests that
Ori 139-409 could be one of the youngest circumbinary rings reported up to
date. Finally, our results confirm that the circumbinary rings are actively
funneling fresh gas material to the central compact binary circumstellar disks,
i.e. to the protostars in the very early phases of their evolution.Comment: Accepted by MNRA
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