386 research outputs found
The Index of (White) Noises and their Product Systems
(See detailed abstract in the article.) We single out the correct class of
spatial product systems (and the spatial endomorphism semigroups with which the
product systems are associated) that allows the most far reaching analogy in
their classifiaction when compared with Arveson systems. The main differences
are that mere existence of a unit is not it sufficient: The unit must be
CENTRAL. And the tensor product under which the index is additive is not
available for product systems of Hilbert modules. It must be replaced by a new
product that even for Arveson systems need not coincide with the tensor
product
Spin Foams and Noncommutative Geometry
We extend the formalism of embedded spin networks and spin foams to include
topological data that encode the underlying three-manifold or four-manifold as
a branched cover. These data are expressed as monodromies, in a way similar to
the encoding of the gravitational field via holonomies. We then describe
convolution algebras of spin networks and spin foams, based on the different
ways in which the same topology can be realized as a branched covering via
covering moves, and on possible composition operations on spin foams. We
illustrate the case of the groupoid algebra of the equivalence relation
determined by covering moves and a 2-semigroupoid algebra arising from a
2-category of spin foams with composition operations corresponding to a fibered
product of the branched coverings and the gluing of cobordisms. The spin foam
amplitudes then give rise to dynamical flows on these algebras, and the
existence of low temperature equilibrium states of Gibbs form is related to
questions on the existence of topological invariants of embedded graphs and
embedded two-complexes with given properties. We end by sketching a possible
approach to combining the spin network and spin foam formalism with matter
within the framework of spectral triples in noncommutative geometry.Comment: 48 pages LaTeX, 30 PDF figure
Extensions of C*-dynamical systems to systems with complete transfer operators
Starting from an arbitrary endomorphism of a unital C*-algebra
we construct a bigger C*-algebra and extend onto in such a way
that the extended endomorphism has a unital kernel and a hereditary
range, i.e. there exists a unique non-degenerate transfer operator for
, called the complete transfer operator. The pair is
universal with respect to a suitable notion of a covariant representation and
depends on a choice of an ideal in . The construction enables a natural
definition of the crossed product for arbitrary .Comment: Compressed and submitted version, 9 page
Weak charge form factor and radius of 208Pb through parity violation in electron scattering
We use distorted wave electron scattering calculations to extract the weak
charge form factor F_W(q), the weak charge radius R_W, and the point neutron
radius R_n, of 208Pb from the PREX parity violating asymmetry measurement. The
form factor is the Fourier transform of the weak charge density at the average
momentum transfer q=0.475 fm. We find F_W(q) =0.204 \pm 0.028 (exp) \pm
0.001 (model). We use the Helm model to infer the weak radius from F_W(q). We
find R_W= 5.826 \pm 0.181 (exp) \pm 0.027 (model) fm. Here the exp error
includes PREX statistical and systematic errors, while the model error
describes the uncertainty in R_W from uncertainties in the surface thickness
\sigma of the weak charge density. The weak radius is larger than the charge
radius, implying a "weak charge skin" where the surface region is relatively
enriched in weak charges compared to (electromagnetic) charges. We extract the
point neutron radius R_n=5.751 \pm 0.175 (exp) \pm 0.026 (model) \pm 0.005
(strange) fm$, from R_W. Here there is only a very small error (strange) from
possible strange quark contributions. We find R_n to be slightly smaller than
R_W because of the nucleon's size. Finally, we find a neutron skin thickness of
R_n-R_p=0.302\pm 0.175 (exp) \pm 0.026 (model) \pm 0.005 (strange) fm, where
R_p is the point proton radius.Comment: 5 pages, 1 figure, published in Phys Rev. C. Only one change in this
version: we have added one author, also to metadat
Precision Electron-Beam Polarimetry using Compton Scattering at 1 GeV
We report on the highest precision yet achieved in the measurement of the
polarization of a low energy, (1 GeV), electron beam, accomplished
using a new polarimeter based on electron-photon scattering, in Hall~C at
Jefferson Lab. A number of technical innovations were necessary, including a
novel method for precise control of the laser polarization in a cavity and a
novel diamond micro-strip detector which was able to capture most of the
spectrum of scattered electrons. The data analysis technique exploited track
finding, the high granularity of the detector and its large acceptance. The
polarization of the A, ~GeV electron beam was measured with a
statistical precision of ~1\% per hour and a systematic uncertainty of
0.59\%. This exceeds the level of precision required by the \qweak experiment,
a measurement of the vector weak charge of the proton. Proposed future
low-energy experiments require polarization uncertainty ~0.4\%, and this
result represents an important demonstration of that possibility. This
measurement is also the first use of diamond detectors for particle tracking in
an experiment.Comment: 9 pages, 7 figures, published in PR
Diagonalizing operators over continuous fields of C*-algebras
It is well known that in the commutative case, i.e. for being a
commutative C*-algebra, compact selfadjoint operators acting on the Hilbert
C*-module (= continuous families of such operators , ) can
be diagonalized if we pass to a bigger W*-algebra which can be obtained from by completing it with respect to the weak
topology. Unlike the "eigenvectors", which have coordinates from , the
"eigenvalues" are continuous, i.e. lie in the C*-algebra . We discuss here
the non-commutative analog of this well-known fact. Here the "eigenvalues" are
defined not uniquely but in some cases they can also be taken from the initial
C*-algebra instead of the bigger W*-algebra. We prove here that such is the
case for some continuous fields of real rank zero C*-algebras over a
one-dimensional manifold and give an example of a C*-algebra for which the
"eigenvalues" cannot be chosen from , i.e. are discontinuous. The main point
of the proof is connected with a problem on almost commuting operators. We
prove that for some C*-algebras if is a selfadjoint, is a
unitary and if the norm of their commutant is small enough then one can
connect with the unity by a path so that the norm of
would be also small along this path.Comment: 21 pages, LaTeX 2.09, no figure
Discovering the New Standard Model: Fundamental Symmetries and Neutrinos
This White Paper describes recent progress and future opportunities in the
area of fundamental symmetries and neutrinos.Comment: Report of the Fundamental Symmetries and Neutrinos Workshop, August
10-11, 2012, Chicago, I
High-Energy Carbon-Ions Implantation - An Attempt to Grow Diamond Inside Copper
1 MeV carbon ions were implanted into single-crystal copper which was then annealed in argon at temperatures ranging from 350 to 750-degrees-C. Regrowth of the radiation-damaged copper was examined by RBS-channeling measurements. Carbon segregation occurred on annealing at 750-degrees-C. Prolonged annealing at 750-degrees-C caused blistering of the copper layer over the buried carbon. After removal of the blistered copper overlayer, the previously buried carbon layer was examined by Raman scattering, showing that graphite is the dominant phase
Quark-Hadron Duality in Neutron (3He) Spin Structure
We present experimental results of the first high-precision test of
quark-hadron duality in the spin-structure function g_1 of the neutron and
He using a polarized 3He target in the four-momentum-transfer-squared range
from 0.7 to 4.0 (GeV/c)^2. Global duality is observed for the spin-structure
function g_1 down to at least Q^2 = 1.8 (GeV/c)^2 in both targets. We have also
formed the photon-nucleon asymmetry A_1 in the resonance region for 3He and
found no strong Q^2-dependence above 2.2 (GeV/c)^2.Comment: 13 pages, 3 figure
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