209 research outputs found
BRST cohomology in Beltrami parametrization
We study the BRST cohomology within a local conformal Lagrangian field theory
model built on a two dimensional Riemann surface with no boundary. We deal with
the case of the complex structure parametrized by Beltrami differential and the
scalar matter fields. The computation of {\em all} elements of the BRST
cohomology is given.Comment: 25 pages, LATE
Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators
The anti-BRST transformation, in its Sp(2)-symmetric version, for the general
case of any stage-reducible gauge theories is implemented in the usual BV
approach. This task is accomplished not by duplicating the gauge symmetries but
rather by duplicating all fields and antifields of the theory and by imposing
the acyclicity of the Koszul-Tate differential. In this way the Sp(2)-covariant
quantization can be realised in the standard BV approach and its equivalence
with BLT quantization can be proven by a special gauge fixing procedure.Comment: 13 pages, Latex, To Be Published in International Journal of Modern
Physics
Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems
An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class
systems based on homological arguments is proposed. The general formalism is
exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page
Quasilinear Schr\"odinger equations II: Small data and cubic nonlinearities
In part I of this project we examined low regularity local well-posedness for
generic quasilinear Schr\"odinger equations with small data. This improved, in
the small data regime, the preceding results of Kenig, Ponce, and Vega as well
as Kenig, Ponce, Rolvung, and Vega. In the setting of quadratic interactions,
the (translation invariant) function spaces which were utilized incorporated an
summability over cubes in order to account for Mizohata's integrability
condition, which is a necessary condition for the well-posedness for the
linearized equation. For cubic interactions, this integrability condition
meshes better with the inherent nature of the Schr\"odinger equation, and
such summability is not required. Thus we are able to prove small data
well-posedness in spaces.Comment: 19 page
Decay estimates for variable coefficient wave equations in exterior domains
In this article we consider variable coefficient, time dependent wave
equations in exterior domains. We prove localized energy estimates if the
domain is star-shaped and global in time Strichartz estimates if the domain is
strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor
correction was made to the proof of Lemma 1
Strichartz estimates on Schwarzschild black hole backgrounds
We study dispersive properties for the wave equation in the Schwarzschild
space-time. The first result we obtain is a local energy estimate. This is then
used, following the spirit of earlier work of Metcalfe-Tataru, in order to
establish global-in-time Strichartz estimates. A considerable part of the paper
is devoted to a precise analysis of solutions near the trapping region, namely
the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place
Concerning the Wave equation on Asymptotically Euclidean Manifolds
We obtain KSS, Strichartz and certain weighted Strichartz estimate for the
wave equation on , , when metric
is non-trapping and approaches the Euclidean metric like with
. Using the KSS estimate, we prove almost global existence for
quadratically semilinear wave equations with small initial data for
and . Also, we establish the Strauss conjecture when the metric is radial
with for .Comment: Final version. To appear in Journal d'Analyse Mathematiqu
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