3,177 research outputs found
Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies
For space-times with two spacelike isometries, we present infinite
hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations
as represented by their Ernst potentials. This hierarchy contains three
arbitrary rational functions of an auxiliary complex parameter. They are
constructed using the so called `monodromy transform' approach and our new
method for the solution of the linear singular integral equation form of the
reduced Einstein equations. The solutions presented, which describe
inhomogeneous cosmological models or gravitational and electromagnetic waves
and their interactions, include a number of important known solutions as
particular cases.Comment: 7 pages, minor correction and reduction to conform with published
versio
The embedding structure and the shift operator of the U(1) lattice current algebra
The structure of block-spin embeddings of the U(1) lattice current algebra is
described. For an odd number of lattice sites, the inner realizations of the
shift automorphism areclassified. We present a particular inner shift operator
which admits a factorization involving quantum dilogarithms analogous to the
results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected;
version to appear in Lett.Math.Phy
On dynamical adjoint functor
We give an explicit formula relating the dynamical adjoint functor and
dynamical twist over nonalbelian base to the invariant pairing on parabolic
Verma modules. As an illustration, we give explicit - and
-invariant star product on projective spaces
Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
For the fields depending on two of the four space-time coordinates only, the
spaces of local solutions of various integrable reductions of Einstein's field
equations are shown to be the subspaces of the spaces of local solutions of the
``null-curvature'' equations constricted by a requirement of a universal (i.e.
solution independent) structures of the canonical Jordan forms of the unknown
matrix variables. These spaces of solutions of the ``null-curvature'' equations
can be parametrized by a finite sets of free functional parameters -- arbitrary
holomorphic (in some local domains) functions of the spectral parameter which
can be interpreted as the monodromy data on the spectral plane of the
fundamental solutions of associated linear systems. Direct and inverse problems
of such mapping (``monodromy transform''), i.e. the problem of finding of the
monodromy data for any local solution of the ``null-curvature'' equations with
given canonical forms, as well as the existence and uniqueness of such solution
for arbitrarily chosen monodromy data are shown to be solvable unambiguously.
The linear singular integral equations solving the inverse problems and the
explicit forms of the monodromy data corresponding to the spaces of solutions
of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction
New Test of Supernova Electron Neutrino Emission using Sudbury Neutrino Observatory Sensitivity to the Diffuse Supernova Neutrino Background
Supernovae are rare nearby, but they are not rare in the Universe, and all
past core-collapse supernovae contributed to the Diffuse Supernova Neutrino
Background (DSNB), for which the near-term detection prospects are very good.
The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux,
cm s, is just above the
range of recent theoretical predictions based on the measured star formation
rate history. We show that the Sudbury Neutrino Observatory should be able to
test the corresponding DSNB electron {\it neutrino} flux with a sensitivity as
low as cm s,
improving the existing Mont Blanc limit by about three orders of magnitude.
While conventional supernova models predict comparable electron neutrino and
antineutrino fluxes, it is often considered that the first (and
forward-directed) SN 1987A event in the Kamiokande-II detector should be
attributed to electron-neutrino scattering with an electron, which would
require a substantially enhanced electron neutrino flux. We show that with the
required enhancements in either the burst or thermal phase fluxes, the
DSNB electron neutrino flux would generally be detectable in the Sudbury
Neutrino Observatory. A direct experimental test could then resolve one of the
enduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals a
serious misunderstanding of supernova physics, or was simply an unlikely
statistical fluctuation. Thus the electron neutrino sensitivity of the Sudbury
Neutrino Observatory is an important complement to the electron antineutrino
sensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
We show that the zeroth cohomology of M. Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber
operad. They are parameterized by grt_1, up to one class (or two, depending on
the definitions). More generally, the homotopy derivations of the (non-unital)
E_n operads may be expressed through the cohomology of a suitable graph
complex. Our methods also give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt_1-elements implies the hexagon
equation
Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method
A new approach to the inverse-scattering technique of Alekseev is presented
which permits real-pole soliton solutions of the Ernst equations to be
considered. This is achieved by adopting distinct real poles in the scattering
matrix and its inverse. For the case in which the electromagnetic field
vanishes, some explicit solutions are given using a Minkowski seed metric. The
relation with the corresponding soliton solutions that can be constructed using
the Belinskii-Zakharov inverse-scattering technique is determined.Comment: 8 pages, LaTe
One-dimensional Chern-Simons theory
We study a one-dimensional toy version of the Chern-Simons theory. We
construct its simplicial version which comprises features of a low-energy
effective gauge theory and of a topological quantum field theory in the sense
of Atiyah.Comment: 37 page
Muon-Induced Background Study for an Argon-Based Long Baseline Neutrino Experiment
We evaluated rates of transversing muons, muon-induced fast neutrons, and
production of Cl and other cosmogenically produced nuclei that pose as
potential sources of background to the physics program proposed for an
argon-based long baseline neutrino experiment at the Sanford Underground
Research Facility (SURF). The Geant4 simulations were carried out with muons
and muon-induced neutrons for both 800 ft (0.712 km.w.e.) and 4850 ft levels
(4.3 km.w.e.). We developed analytic models to independently calculate the
Cl production using the measured muon fluxes at different levels of the
Homestake mine. The muon induced Cl production rates through stopped
muon capture and the muon-induced neutrons and protons via (n,p) and (p,n)
reactions were evaluated. We find that the Monte Carlo simulated production
rates of Cl agree well with the predictions from analytic models. A
depth-dependent parametrization was developed and benchmarked to the direct
analytic models. We conclude that the muon-induced processes will result in
large backgrounds to the physics proposed for an argon-based long baseline
neutrino experiment at a depth of less than 4.0 km.w.e.Comment: 12 pages, 15 figure
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