23,239 research outputs found

### Extending tensors on polar manifolds

Let $M$ be a Riemannian manifold with a polar action by the Lie group $G$,
with section $\Sigma\subset M$ and generalized Weyl group $W$. We show that
restriction to $\Sigma$ is a surjective map from the set of smooth
$G$-invariant tensors on $M$ onto the set of smooth $W$-invariant tensors on
$\Sigma$. Moreover, we show that every smooth $W$-invariant Riemannian metric
on $\Sigma$ can be extended to a smooth $G$-invariant Riemannian metric on $M$
with respect to which the $G$-action remains polar with the same section
$\Sigma$.Comment: arXiv admin note: text overlap with arXiv:1205.476

### Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice

It is well known that, in Landau gauge, the renormalization function of the
ghost-ghost-gluon vertex \widetilde{Z}_1(p^2) is finite and constant, at least
to all orders of perturbation theory. On the other hand, a direct
non-perturbative verification of this result using numerical simulations of
lattice QCD is still missing. Here we present a preliminary numerical study of
the ghost-ghost-gluon vertex and of its corresponding renormalization function
using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained
in 4 dimensions for lattice couplings beta = 2.2, 2.3, 2.4 and lattice sides N
= 4, 8, 16.Comment: 3 pages, 1 figure, presented by A. Mihara at the IX Hadron Physics
and VII Relativistic Aspects of Nuclear Physics Workshops, Angra dos Reis,
Rio de Janeiro, Brazil (March 28--April 3, 2004

### Relative asymptotics for orthogonal matrix polynomials

In this paper we study sequences of matrix polynomials that satisfy a
non-symmetric recurrence relation. To study this kind of sequences we use a
vector interpretation of the matrix orthogonality. In the context of these
sequences of matrix polynomials we introduce the concept of the generalized
matrix Nevai class and we give the ratio asymptotics between two consecutive
polynomials belonging to this class. We study the generalized matrix Chebyshev
polynomials and we deduce its explicit expression as well as we show some
illustrative examples. The concept of a Dirac delta functional is introduced.
We show how the vector model that includes a Dirac delta functional is a
representation of a discrete Sobolev inner product. It also allows to
reinterpret such perturbations in the usual matrix Nevai class. Finally, the
relative asymptotics between a polynomial in the generalized matrix Nevai class
and a polynomial that is orthogonal to a modification of the corresponding
matrix measure by the addition of a Dirac delta functional is deduced

### Temporal correlator in YM^2_3 and reflection-positivity violation

We consider numerical data for the lattice Landau gluon propagator obtained
at very large lattice volumes in three-dimensional pure SU(2) Yang-Mills gauge
theory (YM^2_3). We find that the temporal correlator C(t) shows an oscillatory
pattern and is negative for several values of t. This is an explicit violation
of reflection positivity and can be related to gluon confinement. We also
obtain a good fit for this quantity in the whole time interval using a sum of
Stingl-like propagators.Comment: 3 pages, 1 figure, 1 table, presented by A.R. Taurines at the IX
Hadron Physics and VII Relativistic Aspects of Nuclear Physics Workshops,
Angra dos Reis, Rio de Janeiro, Brazil (March 28--April 3, 2004

- â€¦