2,937 research outputs found
Partially Massless Spin 2 Electrodynamics
We propose that maximal depth, partially massless, higher spin excitations
can mediate charged matter interactions in a de Sitter universe. The proposal
is motivated by similarities between these theories and their traditional
Maxwell counterpart: their propagation is lightlike and corresponds to the same
Laplacian eigenmodes as the de Sitter photon; they are conformal in four
dimensions; their gauge invariance has a single scalar parameter and actions
can be expressed as squares of single derivative curvature tensors. We examine
this proposal in detail for its simplest spin 2 example. We find that it is
possible to construct a natural and consistent interaction scheme to conserved
vector electromagnetic currents primarily coupled to the helicity 1 partially
massless modes. The resulting current-current single ``partial-photon''
exchange amplitude is the (very unCoulombic) sum of contact and shorter-range
terms, so the partial photon cannot replace the traditional one, but rather
modifies short range electromagnetic interactions. We also write the gauge
invariant fourth-derivative effective actions that might appear as effective
corrections to the model, and their contributions to the tree amplitude are
also obtained.Comment: 15 pages, LaTe
Topologically massive gravity as a Pais-Uhlenbeck oscillator
We give a detailed account of the free field spectrum and the Newtonian limit
of the linearized "massive" (Pauli-Fierz), "topologically massive"
(Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski
spacetime. For a certain ratio of the parameters, the linearized free theory is
Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator
which, despite being a higher derivative theory, is ghost-free.Comment: 9 pages, no figures, RevTEX4; version 2: a new paragraph and a
reference added to the Introduction, a new appendix added to review
Pais-Uhlenbeck oscillators; accepted for publication in Class. Quant. Gra
Symmetry Induced 4-Wave Capillary Wave Turbulence
We report theoretical and experimental results on 4-wave capillary wave
turbulence. A system consisting of two inmiscible and incompressible fluids of
the same density can be written in a Hamiltonian way for the conjugated pair
. When given the symmetry , the set of weakly non-linear
interacting waves display a Kolmogorov-Zakharov (KZ) spectrum
in wave vector space. The wave system was studied experimentally with two
inmiscible fluids of almost equal densities (water and silicon oil) where the
capillary surface waves are excited by a low frequency random forcing. The
power spectral density (PSD) and probability density function (PDF) of the
local wave amplitude are studied. Both theoretical and experimental results are
in fairly good agreement with each other.Comment: 6 pages, 2 figure
Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter
Stabilization of a light bullet in a layered Kerr medium with sign-changing nonlinearity
Using the numerical solution of the nonlinear Schr\"odinger equation and a
variational method it is shown that (3+1)-dimensional spatiotemporal optical
solitons, known as light bullets, can be stabilized in a layered Kerr medium
with sign-changing nonlinearity along the propagation direction.Comment: 4 pages, 3 PS figure
On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields
It was shown recently that Frobenius reduction of the matrix fields reveals
interesting relations among the nonlinear Partial Differential Equations (PDEs)
integrable by the Inverse Spectral Transform Method (-integrable PDEs),
linearizable by the
Hoph-Cole substitution (-integrable PDEs) and integrable by the method of
characteristics (-integrable PDEs). However, only two classes of
-integrable PDEs have been involved: soliton equations like Korteweg-de
Vries, Nonlinear Shr\"odinger, Kadomtsev-Petviashvili and Davey-Stewartson
equations, and GL(N,\CC) Self-dual type PDEs, like Yang-Mills equation. In
this paper we consider the simple five-dimensional nonlinear PDE from another
class of -integrable PDEs, namely, scalar nonlinear PDE which is
commutativity condition of the pair of vector fields. We show its origin from
the (1+1)-dimensional hierarchy of -integrable PDEs after certain
composition of Frobenius type and differential reductions imposed on the matrix
fields. Matrix generalization of the above scalar nonlinear PDE will be derived
as well.Comment: 14 pages, 1 figur
Localized eigenmodes of the covariant lattice Laplacian
We study numerically the eigenmode spectrum of the covariant lattice
Laplacian, in the fundamental SU(2) color group representation. It is found
that eigenmodes at the lower and upper ends of the spectrum are localized, and
that the localization volume scales. In contrast, the eigenmodes of the lattice
Faddeev-Popov operator are all extended rather than localized (as required for
confinement) despite the similarity of the kinetic and Faddeev-Popov operators.Comment: Talk presented by J. Greensite at Lattice2005 (Topology and
Confinement), Dublin, July 25-30, 2005; 6 pages, 4 figures, uses PoS.cls; to
appear in Proceedings of Scienc
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