1,236 research outputs found
Complete quantization of a diffeomorphism invariant field theory
In order to test the canonical quantization programme for general relativity
we introduce a reduced model for a real sector of complexified Ashtekar gravity
which captures important properties of the full theory. While it does not
correspond to a subset of Einstein's gravity it has the advantage that the
programme of canonical quantization can be carried out completely and
explicitly, both, via the reduced phase space approach or along the lines of
the algebraic quantization programme. This model stands in close correspondence
to the frequently treated cylindrically symmetric waves. In contrast to other
models that have been looked at up to now in terms of the new variables the
reduced phase space is infinite dimensional while the scalar constraint is
genuinely bilinear in the momenta. The infinite number of Dirac observables can
be expressed in compact and explicit form in terms of the original phase space
variables. They turn out, as expected, to be non-local and form naturally a set
of countable cardinality.Comment: 32p, LATE
Hermitian vector fields and special phase functions
We start by analysing the Lie algebra of Hermitian vector fields of a
Hermitian line bundle.
Then, we specify the base space of the above bundle by considering a Galilei,
or an Einstein spacetime. Namely, in the first case, we consider, a fibred
manifold over absolute time equipped with a spacelike Riemannian metric, a
spacetime connection (preserving the time fibring and the spacelike metric) and
an electromagnetic field. In the second case, we consider a spacetime equipped
with a Lorentzian metric and an electromagnetic field.
In both cases, we exhibit a natural Lie algebra of special phase functions
and show that the Lie algebra of Hermitian vector fields turns out to be
naturally isomorphic to the Lie algebra of special phase functions.
Eventually, we compare the Galilei and Einstein cases
Mechanical similarity as a generalization of scale symmetry
In this paper we study the symmetry known as mechanical similarity (LMS) and
present for any monomial potential. We analyze it in the framework of the
Koopman-von Neumann formulation of classical mechanics and prove that in this
framework the LMS can be given a canonical implementation. We also show that
the LMS is a generalization of the scale symmetry which is present only for the
inverse square potential. Finally we study the main obstructions which one
encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde
Modelling intrusions through quiescent and moving ambients
Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these plumes cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, and in this paper we develop a shallow-layer model that governs their motion. We couple this dynamical model to a model for particle transport and sedimentation, to predict both the time-dependent distribution of ash within volcanic intrusions and the flux of ash that falls towards the ground. In an otherwise quiescent atmosphere, the intrusions spread axisymmetrically. We find that the buoyancy-inertial scalings previously identified for continuously supplied axisymmetric intrusions are not realised by solutions of the governing equations. By calculating asymptotic solutions to our model we show that the flow is not self-similar, but is instead time-dependent only in a narrow region at the front of the intrusion. This non-self-similar behaviour results in the radius of the intrusion growing with time \textrm3/4 as suggested previously. We also identify a transition to drag-dominated flow, which is described by a similarity solution with radial growth now proportional to \textrm5/9$ . In the presence of an ambient wind, intrusions are not axisymmetric. Instead, they are predominantly advected downstream, while at the same time spreading laterally and thinning vertically due to persistent buoyancy forces. We show that close to the source, this lateral spreading is in a buoyancy-inertial regime, whereas far downwind, the horizontal buoyancy forces that drive the spreading are balanced by drag. Our results emphasise the important role of buoyancy-driven spreading, even at large distances from the source, in the formation of the flowing thin horizontally extensive layers of ash that form in the atmosphere as a result of volcanic eruptions
Duality through the symplectic embedding formalism
In this work we show that we can obtain dual equivalent actions following the
symplectic formalism with the introduction of extra variables which enlarge the
phase space. We show that the results are equal as the one obtained with the
recently developed gauging iterative Noether dualization method (NDM). We
believe that, with the arbitrariness property of the zero mode, the symplectic
embedding method (SEM) is more profound since it can reveal a whole family of
dual equivalent actions. We illustrate the method demonstrating that the
gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the
introduction of an explicit mass term and a topological term can be restored to
obtain the dual equivalent and gauge-invariant version of the theory.Comment: RevTeX4, 10 pages. To appear in Int. J. Mod. Phys.
Hamiltonian symplectic embedding of the massive noncommutative U(1) Theory
We show that the massive noncommutative U(1) theory is embedded in a gauge
theory using an alternative systematic way, which is based on the symplectic
framework. The embedded Hamiltonian density is obtained after a finite number
of steps in the iterative symplectic process, oppositely to the result proposed
using the BFFT formalism. This alternative formalism of embedding shows how to
get a set of dynamically equivalent embedded Hamiltonian densities.Comment: 16 pages, no figures, revtex4, corrected version, references
additione
Interaction between volcanic plumes and wind during the 2010 Eyjafjallajokull eruption, Iceland
Natural and projectively equivariant quantizations by means of Cartan Connections
The existence of a natural and projectively equivariant quantization in the
sense of Lecomte [20] was proved recently by M. Bordemann [4], using the
framework of Thomas-Whitehead connections. We give a new proof of existence
using the notion of Cartan projective connections and we obtain an explicit
formula in terms of these connections. Our method yields the existence of a
projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant
quantization exists in the flat situation in the sense of [18], thus solving
one of the problems left open by M. Bordemann.Comment: 13 page
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