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