49,560 research outputs found
Coulomb Confinement from the Yang-Mills Vacuum State in 2+1 Dimensions
The Coulomb-gauge ghost propagator, and the color-Coulomb potential, are
computed in an ensemble of configurations derived from our recently proposed
Yang-Mills vacuum wavefunctional in 2+1 dimensions. The results are compared to
the corresponding values obtained by standard Monte Carlo simulations in three
Euclidean dimensions. The agreement is quite striking for the Coulomb-gauge
ghost propagator. The color-Coulomb potential rises linearly at large
distances, but its determination suffers from rather large statistical
fluctuations, due to configurations with very low values of , the lowest
eigenvalue of the Coulomb-gauge Faddeev-Popov operator. However, if one imposes
cuts on the data, effectively leaving out configurations with very low ,
the agreement of the potential in both sets of configurations is again
satisfactory, although the errorbars grow systematically as the cutoff is
eliminated.Comment: 8 pages, 5 figures (10 EPS files), RevTeX4.1. V2: original figs. 4
and 5 compressed into a new fig. 5; a new fig. 4; sec. IV.B slightly modified
to reflect the changes. Version to appear in Phys. Rev. D. V3: a reference
corrected
Model as a Topological Description of String Theory
We study the model coupled to topological gravity as a candidate
to describing string theory at the self-dual radius. We define the model
by analytical continuation of topological recursion relations to .
We show that at genus zero the recursion relations yield the
Ward identities for tachyon correlators on the sphere. A scheme
for computing correlation functions of gravitational descendants is
proposed and applied for the computation of several correlators. It is
suggested that the latter correspond to correlators of discrete states of the
string. In a similar manner to the models, we show that there exist
topological recursion relations for the correlators in the theory that
consist of only one and two splittings of the Riemann surface. Using a
postulated regularized contact, we prove that the genus one recursion
relations for tachyon correlators coincide with the Ward
identities on the torus. We argue that the structure of these recursion
relations coincides with that of the Ward identities for any
genus.Comment: 39 pages,latex,taup-2170 -9
Getting more flavour out of one-flavour QCD
We argue that no notion of flavour is necessary when performing amplitude
calculations in perturbative QCD with massless quarks. We show this explicitly
at tree-level, using a flavour recursion relation to obtain multi-flavoured QCD
from one-flavour QCD. The method relies on performing a colour decomposition,
under which the one-flavour primitive amplitudes have a structure which is
restricted by planarity and cyclic ordering. An understanding of SU(3)_c group
theory relations between QCD primitive amplitudes and their organisation around
the concept of a Dyck tree is also necessary. The one-flavour primitive
amplitudes are effectively N=1 supersymmetric, and a simple consequence is that
all of tree-level massless QCD can be obtained from Drummond and Henn's closed
form solution to tree-level N=4 super Yang-Mills theory.Comment: 27 pages, 6 figure
Nijenhuis operator in contact homology and descendant recursion in symplectic field theory
In this paper we investigate the algebraic structure related to a new type of
correlator associated to the moduli spaces of -parametrized curves in
contact homology and rational symplectic field theory. Such correlators are the
natural generalization of the non-equivariant linearized contact homology
differential (after Bourgeois-Oancea) and give rise to an invariant Nijenhuis
(or hereditary) operator (\`a la Magri-Fuchssteiner) in contact homology which
recovers the descendant theory from the primaries. We also sketch how such
structure generalizes to the full SFT Poisson homology algebra to a (graded
symmetric) bivector. The descendant hamiltonians satisfy to recursion
relations, analogous to bihamiltonian recursion, with respect to the pair
formed by the natural Poisson structure in SFT and such bivector. In case the
target manifold is the product stable Hamiltonian structure , with
a symplectic manifold, the recursion coincides with genus topological
recursion relations in the Gromov-Witten theory of .Comment: 30 pages, 3 figure
Efficient Recursion Method for Inverting Overlap Matrix
A new O(N) algorithm based on a recursion method, in which the computational
effort is proportional to the number of atoms N, is presented for calculating
the inverse of an overlap matrix which is needed in electronic structure
calculations with the the non-orthogonal localized basis set. This efficient
inverting method can be incorporated in several O(N) methods for
diagonalization of a generalized secular equation. By studying convergence
properties of the 1-norm of an error matrix for diamond and fcc Al, this method
is compared to three other O(N) methods (the divide method, Taylor expansion
method, and Hotelling's method) with regard to computational accuracy and
efficiency within the density functional theory. The test calculations show
that the new method is about one-hundred times faster than the divide method in
computational time to achieve the same convergence for both diamond and fcc Al,
while the Taylor expansion method and Hotelling's method suffer from numerical
instabilities in most cases.Comment: 17 pages and 4 figure
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