2,964 research outputs found
A tour on Hermitian symmetric manifolds
Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous
and such that every point has a symmetry preserving the Hermitian structure.
The aim of these notes is to present an introduction to this important class of
manifolds, trying to survey the several different perspectives from which
Hermitian symmetric manifolds can be studied.Comment: 56 pages, expanded version. Written for the Proceedings of the
CIME-CIRM summer course "Combinatorial Algebraic Geometry". Comments are
still welcome
The twin paradox in compact spaces
Twins travelling at constant relative velocity will each see the other's time
dilate leading to the apparent paradox that each twin believes the other ages
more slowly. In a finite space, the twins can both be on inertial, periodic
orbits so that they have the opportunity to compare their ages when their paths
cross. As we show, they will agree on their respective ages and avoid the
paradox. The resolution relies on the selection of a preferred frame singled
out by the topology of the space.Comment: to be published in PRA, 3 page
Non-BPS Solutions of the Noncommutative CP^1 Model in 2+1 Dimensions
We find non-BPS solutions of the noncommutative CP^1 model in 2+1 dimensions.
These solutions correspond to soliton anti-soliton configurations. We show that
the one-soliton one-anti-soliton solution is unstable when the distance between
the soliton and the anti-soliton is small. We also construct time-dependent
solutions and other types of solutions.Comment: 11 pages, minor correction
Connecting geodesics and security of configurations in compact locally symmetric spaces
A pair of points in a riemannian manifold makes a secure configuration if the
totality of geodesics connecting them can be blocked by a finite set. The
manifold is secure if every configuration is secure. We investigate the
security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure
Eternity and the cosmological constant
The purpose of this paper is to analyze the stability of interacting matter
in the presence of a cosmological constant. Using an approach based on the heat
equation, no imaginary part is found for the effective potential in the
presence of a fixed background, which is the n-dimensional sphere or else an
analytical continuation thereof, which is explored in some detail.Comment: 45 pages, 6 figure
Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics
In this work we outline the two most commonly used test theories (RMS and
SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop
the general framework of applying these test theories to resonator experiments
with an emphasis on rotating experiments in the laboratory. We compare the
inherent sensitivity factors of common experiments and propose some new
configurations. Finally we apply the test theories to the rotating cryogenic
experiment at the University of Western Australia, which recently set new
limits in both the RMS and SME frameworks [hep-ph/0506074].Comment: Submitted to Lecture Notes in Physics, 36 pages, minor modifications,
updated list of reference
Harmonic maps from degenerating Riemann surfaces
We study harmonic maps from degenerating Riemann surfaces with uniformly
bounded energy and show the so-called generalized energy identity. We find
conditions that are both necessary and sufficient for the compactness in
and modulo bubbles of sequences of such maps.Comment: 27 page
Spin splitting and precession in quantum dots with spin-orbit coupling: the role of spatial deformation
Extending a previous work on spin precession in GaAs/AlGaAs quantum dots with
spin-orbit coupling, we study the role of deformation in the external
confinement. Small elliptical deformations are enough to alter the precessional
characteristics at low magnetic fields. We obtain approximate expressions for
the modified factor including weak Rashba and Dresselhaus spin-orbit terms.
For more intense couplings numerical calculations are performed. We also study
the influence of the magnetic field orientation on the spin splitting and the
related anisotropy of the factor. Using realistic spin-orbit strengths our
model calculations can reproduce the experimental spin-splittings reported by
Hanson et al. (cond-mat/0303139) for a one-electron dot. For dots containing
more electrons, Coulomb interaction effects are estimated within the
local-spin-density approximation, showing that many features of the
non-iteracting system are qualitatively preserved.Comment: 7 pages, 7 figure
B^F Theory and Flat Spacetimes
We propose a reduced constrained Hamiltonian formalism for the exactly
soluble theory of flat connections and closed two-forms over
manifolds with topology . The reduced phase space
variables are the holonomies of a flat connection for loops which form a basis
of the first homotopy group , and elements of the second
cohomology group of with value in the Lie algebra . When
, and if the two-form can be expressed as , for some
vierbein field , then the variables represent a flat spacetime. This is not
always possible: We show that the solutions of the theory generally represent
spacetimes with ``global torsion''. We describe the dynamical evolution of
spacetimes with and without global torsion, and classify the flat spacetimes
which admit a locally homogeneous foliation, following Thurston's
classification of geometric structures.Comment: 21 pp., Mexico Preprint ICN-UNAM-93-1
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