6,555 research outputs found
Light-Ray Radon Transform for Abelianin and Nonabelian Connection in 3 and 4 Dimensional Space with Minkowsky Metric
We consider a real manifold of dimension 3 or 4 with Minkovsky metric, and
with a connection for a trivial GL(n,C) bundle over that manifold. To each
light ray on the manifold we assign the data of paralel transport along that
light ray. It turns out that these data are not enough to reconstruct the
connection, but we can add more data, which depend now not from lines but from
2-planes, and which in some sence are the data of parallel transport in the
complex light-like directions, then we can reconstruct the connection up to a
gauge transformation. There are some interesting applications of the
construction: 1) in 4 dimensions, the self-dual Yang Mills equations can be
written as the zero curvature condition for a pair of certain first order
differential operators; one of the operators in the pair is the covariant
derivative in complex light-like direction we studied. 2) there is a relation
of this Radon transform with the supersymmetry. 3)using our Radon transform, we
can get a measure on the space of 2 dimensional planes in 4 dimensional real
space. Any such measure give rise to a Crofton 2-density. The integrals of this
2-density over surfaces in R^4 give rise to the Lagrangian for maps of real
surfaces into R^4, and therefore to some string theory. 4) there are relations
with the representation theory. In particular, a closely related transform in 3
dimensions can be used to get the Plancerel formula for representations of
SL(2,R).Comment: We add an important discussion part, establishing the relation of our
Radon transform with the self-dual Yang-Mills, string theory, and the
represntation theory of the group SL(2,R
SU(3) Anderson impurity model: A numerical renormalization group approach exploiting non-Abelian symmetries
We show how the density-matrix numerical renormalization group (DM-NRG)
method can be used in combination with non-Abelian symmetries such as SU(N),
where the decomposition of the direct product of two irreducible
representations requires the use of a so-called outer multiplicity label. We
apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze
the finite size spectrum, determine local fermionic, spin, superconducting, and
trion spectral functions, and also compute the temperature dependence of the
conductance. Our calculations reveal a rich Fermi liquid structure.Comment: 18 pages, 9 figure
The Associated Metric for a Particle in a Quantum Energy Level
We show that the probabilistic distribution over the space in the spectator
world, can be associated via noncommutative geometry (with some modifications)
to a metric in which the particle lives. According to this geometrical view,
the metric in the particle world is ``contracted'' or ``stretched'' in an
inverse proportion to the probability distribution.Comment: 14 pages, latex, epsf, 3 figures. Some clarifications were adde
Convergent expansions for properties of the Heisenberg model for CaVO
We have carried out a wide range of calculations for the Heisenberg
model with nearest- and second-neighbor interactions on a two-dimensional
lattice which describes the geometry of the vanadium ions in the spin-gap
system CaVO. The methods used were convergent high-order perturbation
expansions (``Ising'' and ``Plaquette'' expansions at , as well as
high-temperature expansions) for quantities such as the uniform susceptibility,
sublattice magnetization, and triplet elementary excitation spectrum.
Comparison with the data for CaVO indicates that its magnetic
properties are well described by nearest-neighbor exchange of about 200K in
conjunction with second-neighbor exchange of about 100K.Comment: Uses REVTEX macros. Four pages in two-column format, five postscript
figures. Files packaged using uufile
Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
We consider the Lie group generated by the Lie algebra
of -Minkowski space. Imposing the invariance of the metric under the
pull-back of diffeomorphisms induced by right translations in the group, we
show that a unique right invariant metric is associated with
. This metric coincides with the metric of de Sitter
space-time. We analyze the structure of unitary representations of the group
relevant for the realization of the non-commutative
-Minkowski space by embedding into -dimensional Heisenberg
algebra. Using a suitable set of generalized coherent states, we select the
particular Hilbert space and realize the non-commutative -Minkowski
space as an algebra of the Hilbert-Schmidt operators. We define dequantization
map and fuzzy variant of the Laplace-Beltrami operator such that dequantization
map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami
operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der
Physik by a note and references added and adjuste
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