1,028 research outputs found
Some Weyl modules of the algebraic groups of type
Let be a simple algebraic group of type over an algebraically
closed field of characteristic . We determine the submodule structure of
the Weyl modul es with highest weight for , where
is the fundamental weight of the standard -dimensional module.
In the process, the structures of other Weyl modules with highest weights
linked to are also found. %We also give some computations for the
Weyl modules with highest weights %of the form , which
arise in the study of %the graph automorphism and associated twisted finite
groups.Comment: 25 page
The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
The resummation of soft gluon exchange for QCD hard scattering requires a
matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2
to n massless processes for the first time at two loops. Using color generator
notation, we show that it is proportional to the one-loop matrix. This result
reproduces all pole terms in dimensional regularization of the explicit
calculations of massless 2 to 2 amplitudes in the literature, and it predicts
all poles at next-to-next-to-leading order in any 2 to n process that has been
computed at next-to-leading order. The proportionality of the one- and two-loop
matrices makes possible the resummation in closed form of the
next-to-next-to-leading logarithms and poles in dimensional regularization for
the 2 to n processes.Comment: 5 pages, 1 figure, revte
Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model
To analyze linear field equations on a locally homogeneous spacetime by means
of separation of variables, it is necessary to set up appropriate harmonics
according to its symmetry group. In this paper, the harmonics are presented for
a spatially compactified Bianchi II cosmological model -- the nilgeometric
model. Based on the group structure of the Bianchi II group (also known as the
Heisenberg group) and the compactified spatial topology, the irreducible
differential regular representations and the multiplicity of each irreducible
representation, as well as the explicit form of the harmonics are all
completely determined. They are also extended to vector harmonics. It is
demonstrated that the Klein-Gordon and Maxwell equations actually reduce to
systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM
Two-loop electroweak next-to-leading logarithmic corrections to massless fermionic processes
We consider two-loop leading and next-to-leading logarithmic virtual
corrections to arbitrary processes with external massless fermions in the
electroweak Standard Model at energies well above the electroweak scale. Using
the sector-decomposition method and alternatively the strategy of regions we
calculate the mass singularities that arise as logarithms of Q^2/MW^2, where Q
is the energy scale of the considered process, and 1/\epsilon poles in
D=4-2\epsilon dimensions, to one- and two-loop next-to-leading logarithmic
accuracy. The derivations are performed within the complete electroweak theory
with spontaneous symmetry breaking. Our results indicate a close analogy
between the form of two-loop electroweak logarithmic corrections and the
singular structure of scattering amplitudes in massless QCD. We find agreement
with the resummation prescriptions that have been proposed in the literature
based on a symmetric SU(2) \times U(1) theory matched with QED at the
electroweak scale and provide new next-to-leading contributions proportional to
ln(MZ^2/MW^2).Comment: 63 pages, LaTeX, references updated, some typos corrected, version to
appear in Nucl. Phys.
Gewebedopplersonographie des fetalen Herzens:Untersuchungen zur myokardialen Kontraktionsgeschwindigkeit in verschiedenen Bereichen des rechten und linken Ventrikels gesunder Feten im zweiten Trimenon
In unserer Pilotstudie ist erstmals die Anwendung eines High-end-Ultraschallsystems zur Erstellung qualitativ hochwertiger Kurvenprofile mittels Colour-TDI geprüft worden. Bei 20 Feten wurden im longitudinalen Vierkammerblick Untersuchungen zur Kontraktionsgeschwindigkeit in verschiedenen Phasen des Herzzyklus durchgeführt. Messungen wurden in beiden Ventrikeln und im Septum auf basaler, mittiger und apikaler Ebene vorgenommen. Velocity, Strain und Displacement sind in einer mit der Erwachsenenkardiologie vergleichbaren Qualität darstellbar. Im inter- und intraventrikulären Vergleich bestehen signifikante Unterschiede der Kontraktionsgeschwindigkeit und der Gewebeauslenkung, die physiologisch begründbar sind, während regionale Unterschiede der myokardialen Verformung nicht das geforderte Signifikanzniveau (p<0.05) erreichen. Die von uns aufgezeigten Unterschiede in der regionalen Funktion müssen bei Anwendung des Gewebedopplers in der Pränataldiagnostik stets Berücksichtigung finden
Finite-dimensional representations of twisted hyper loop algebras
We investigate the category of finite-dimensional representations of twisted
hyper loop algebras, i.e., the hyperalgebras associated to twisted loop
algebras over finite-dimensional simple Lie algebras. The main results are the
classification of the irreducible modules, the definition of the universal
highest-weight modules, called the Weyl modules, and, under a certain mild
restriction on the characteristic of the ground field, a proof that the simple
modules and the Weyl modules for the twisted hyper loop algebras are isomorphic
to appropriate simple and Weyl modules for the non-twisted hyper loop algebras,
respectively, via restriction of the action
Scaling Solutions and reconstruction of Scalar Field Potentials
Starting from the hypothesis of scaling solutions, the general exact form of
the scalar field potential is found. In the case of two fluids, it turns out to
be a negative power of hyperbolic sine. In the case of three fluids the
analytic form is not found, but is obtained by quadratures.Comment: 5 pages, 2 figures, some changes in references and figures caption
A new proof of the Bianchi type IX attractor theorem
We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state. The
`Bianchi type IX attractor theorem' states that the past asymptotic behavior of
generic type IX solutions is governed by Bianchi type I and II vacuum states
(Mixmaster attractor). We give a comparatively short and self-contained new
proof of this theorem. The proof we give is interesting in itself, but more
importantly it illustrates and emphasizes that type IX is special, and to some
extent misleading when one considers the broader context of generic models
without symmetries.Comment: 26 pages, 5 figure
Electrocardiogram of the Mixmaster Universe
The Mixmaster dynamics is revisited in a new light as revealing a series of
transitions in the complex scale invariant scalar invariant of the Weyl
curvature tensor best represented by the speciality index , which
gives a 4-dimensional measure of the evolution of the spacetime independent of
all the 3-dimensional gauge-dependent variables except for the time used to
parametrize it. Its graph versus time characterized by correlated isolated
pulses in its real and imaginary parts corresponding to curvature wall
collisions serves as a sort of electrocardiogram of the Mixmaster universe,
with each such pulse pair arising from a single circuit or ``complex pulse''
around the origin in the complex plane. These pulses in the speciality index
and their limiting points on the real axis seem to invariantly characterize
some of the so called spike solutions in inhomogeneous cosmology and should
play an important role as a gauge invariant lens through which to view current
investigations of inhomogeneous Mixmaster dynamics.Comment: version 3: 20 pages iopart style, 19 eps figure files for 8 latex
figures; added example of a transient true spike to contrast with the
permanent true spike example from the Lim family of true spike solutions;
remarks in introduction and conclusion adjusted and toned down; minor
adjustments to the remaining tex
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