792,965 research outputs found
U-branes and T^3 fibrations
We describe eight-dimensional vacuum configurations with varying moduli
consistent with the U-duality group . Focusing on the
latter less-well understood SL(3,Z) properties, we construct a class of
fivebrane solutions living on lines on a three-dimensional base space. The
resulting U-manifolds, with five scalars transforming under SL(3), admit a
Ricci-flat Kahler metric. Based on the connection with special lagrangian
fibered Calabi-Yau 3-folds, this construction provides a simple framework for
the investigation of Calabi-Yau mirrors.Comment: 21 pages, harvma
Quantum Gowdy model: A unitary description
The quantization of the family of linearly polarized Gowdy spacetimes
is discussed in detail, starting with a canonical analysis in which the true
degrees of freedom are described by a scalar field that satisfies a
Klein-Gordon type equation in a fiducial time dependent background. A time
dependent canonical transformation, which amounts to a change of the basic
(scalar) field of the model, brings the system to a description in terms of a
Klein-Gordon equation on a background that is now static, although subject to a
time dependent potential. The system is quantized by means of a natural choice
of annihilation and creation operators. The quantum time evolution is
considered and shown to be unitary, allowing both the Schr\"odinger and
Heisenberg pictures to be consistently constructed. This has to be contrasted
with previous treatments for which time evolution failed to be implementable as
a unitary transformation. Possible implications for both canonical quantum
gravity and quantum field theory in curved spacetime are commented
Free Turbulence on R^3 and T^3
The hydrodynamics of Newtonian fluids has been the subject of a tremendous
amount of work over the past eighty years, both in physics and mathematics.
Sadly, however, a mutual feeling of incomprehension has often hindered
scientific contacts. This article provides a dictionary that allows
mathematicians to define and study the spectral properties of Kolmogorov-Obukov
turbulence in a simple deterministic manner. In other words, this approach fits
turbulence into the mathematical framework of studying the qualitative
properties of solutions of PDEs, independently from any a-priori model of the
structure of the flow. To check that this new approach is correct, this article
proves some of the classical statements that can be found in physics textbooks.
This is followed by an investigation of the compatibility between turbulence
and the smoothness of solutions of Navier-Stokes in 3D, which was the initial
motivation of this study.Comment: 47 pages, 6 figure
The energy-critical defocusing NLS on T^3
We prove global well-posedness in H^1(T^3) for the energy-critical defocusing
NLS.Comment: 24 page
Quantum Gowdy model: A uniqueness result
Modulo a homogeneous degree of freedom and a global constraint, the linearly
polarised Gowdy cosmologies are equivalent to a free scalar field
propagating in a fixed nonstationary background. Recently, a new field
parameterisation was proposed for the metric of the Gowdy spacetimes such that
the associated scalar field evolves in a flat background in 1+1 dimensions with
the spatial topology of , although subject to a time dependent potential.
Introducing a suitable Fock quantisation for this scalar field, a quantum
theory was constructed for the Gowdy model in which the dynamics is implemented
as a unitary transformation. A question that was left open is whether one might
adopt a different, nonequivalent Fock representation by selecting a distinct
complex structure. The present work proves that the chosen Fock quantisation is
in fact unique (up to unitary equivalence) if one demands unitary
implementation of the dynamics and invariance under the group of constant
translations. These translations are precisely those generated by the global
constraint that remains on the Gowdy model. It is also shown that the proof of
uniqueness in the choice of complex structure can be applied to more general
field dynamics than that corresponding to the Gowdy cosmologies.Comment: 28 pages, minor changes, version accepted for publication in
Classical and Quantum Gravit
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