1,195 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
On generalized Abelian deformations
We study sun-products on , i.e. generalized Abelian deformations
associated with star-products for general Poisson structures on . We show
that their cochains are given by differential operators. As a consequence, the
weak triviality of sun-products is established and we show that strong
equivalence classes are quite small. When the Poisson structure is linear
(i.e., on the dual of a Lie algebra), we show that the differentiability of
sun-products implies that covariant star-products on the dual of any Lie
algebra are equivalent each other.Comment: LaTeX 16 pages. To be published in Reviews in Mathematical Physic
On deformation of Poisson manifolds of hydrodynamic type
We study a class of deformations of infinite-dimensional Poisson manifolds of
hydrodynamic type which are of interest in the theory of Frobenius manifolds.
We prove two results. First, we show that the second cohomology group of these
manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial.
Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous
formal deformations of the above manifolds.Comment: LaTeX file, 24 page
Covariant form of the ideal magnetohydrodynamic "connection theorem" in a relativistic plasma
The magnetic connection theorem of ideal Magnetohydrodynamics by Newcomb
[Newcomb W.A., Ann. Phys., 3, 347 (1958)] and its covariant formulation are
rederived and reinterpreted in terms of a "time resetting" projection that
accounts for the loss of simultaneity in different reference frames between
spatially separated events.Comment: 3 pages- 0 figures EPL, accepted in pres
Canonical connection on a class of Riemannian almost product manifolds
The canonical connection on a Riemannian almost product manifold is an
analogue to the Hermitian connection on an almost Hermitian manifold. In this
paper we consider the canonical connection on a class of Riemannian almost
product manifolds with non-integrable almost product structure. We construct
and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012
Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity
We discuss corrections to the ratio of shear viscosity to entropy density
in higher-derivative gravity theories. Generically, these theories
contain ghost modes with Planck-scale masses. Motivated by general
considerations about unitarity, we propose new boundary conditions for the
equations of motion of the graviton perturbations that force the amplitude of
the ghosts modes to vanish. We analyze explicitly four-derivative perturbative
corrections to Einstein gravity which generically lead to four-derivative
equations of motion, compare our choice of boundary conditions to previous
proposals and show that, with our new prescription, the ratio remains
at the Einstein-gravity value of to leading order in the corrections.
It is argued that, when the new boundary conditions are imposed on six and
higher-derivative equations of motion, can only increase from the
Einstein-gravity value. We also recall some general arguments that support the
validity of our results to all orders in the strength of the corrections to
Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity,
for which the equations of motion are only of two-derivative order and the
value of can decrease below when treated in a nonperturbative
way. Our findings provide further evidence for the validity of the KSS bound
for theories that can be viewed as perturbative corrections to Einstein
Gravity.Comment: Sign error in the equations of motion corrected, leading to several
numerical changes. Clarifications added, references added. Main results and
cnclusions essentially unchanged. V3 published version. Clarifications added,
discussion of Gauss-Bonnet moved to main tex
Dirac eigenvalues and total scalar curvature
It has recently been conjectured that the eigenvalues of the Dirac
operator on a closed Riemannian spin manifold of dimension can be
estimated from below by the total scalar curvature: We show by example that such
an estimate is impossible.Comment: 9 pages, LaTeX, uses pstricks macro package. to appear in Journal of
Geometry and Physic
Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds
On a Riemannian almost product manifold we consider a linear
connection preserving the almost product structure and the Riemannian
metric and having a totally skew-symmetric torsion. We determine the class
of the manifolds admitting such a connection and prove that this
connection is unique in terms of the covariant derivative of with respect
to the Levi-Civita connection. We find a necessary and sufficient condition the
curvature tensor of the considered connection to have similar properties like
the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the
case when the torsion of the connection is parallel. We consider this
connection on a Riemannian almost product manifold constructed by a
Lie group .Comment: 14 pages, a revised edition, an example is adde
A rigidity theorem for nonvacuum initial data
In this note we prove a theorem on non-vacuum initial data for general
relativity. The result presents a ``rigidity phenomenon'' for the extrinsic
curvature, caused by the non-positive scalar curvature.
More precisely, we state that in the case of asymptotically flat non-vacuum
initial data if the metric has everywhere non-positive scalar curvature then
the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no
figure
Generalized Lie bialgebroids and Jacobi structures
The notion of a generalized Lie bialgebroid (a generalization of the notion
of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has
associated a canonical generalized Lie bialgebroid. As a kind of converse, we
prove that a Jacobi structure can be defined on the base space of a generalized
Lie bialgebroid. We also show that it is possible to construct a Lie
bialgebroid from a generalized Lie bialgebroid and, as a consequence, we deduce
a duality theorem. Finally, some special classes of generalized Lie
bialgebroids are considered: triangular generalized Lie bialgebroids and
generalized Lie bialgebras.Comment: 32 page
- …