3,598 research outputs found
The scaling dimension of low lying Dirac eigenmodes and of the topological charge density
As a quantitative measure of localization, the inverse participation ratio of
low lying Dirac eigenmodes and topological charge density is calculated on
quenched lattices over a wide range of lattice spacings and volumes. Since
different topological objects (instantons, vortices, monopoles, and artifacts)
have different co-dimension, scaling analysis provides information on the
amount of each present and their correlation with the localization of low lying
eigenmodes.Comment: Lattice2004(topology), Fermilab, June 21 - 26, 2004; 3 pages, 3
figure
Generalized coordinates on the phase space of Yang-Mills theory
We study the suitability of complex Wilson loop variables as (generalized)
coordinates on the physical phase space of -Yang-Mills theory. To this
end, we construct a natural one-to-one map from the physical phase space of the
Yang-Mills theory with compact gauge group to a subspace of the physical
configuration space of the complex G^\C-Yang-Mills theory. Together with a
recent result by Ashtekar and Lewandowski this implies that the complex Wilson
loop variables form a complete set of generalized coordinates on the physical
phase space of -Yang-Mills theory. They also form a generalized
canonical loop algebra. Implications for both general relativity and gauge
theory are discussed.Comment: TeX, 11pp, revised version (minor clarifications added, Comment after
(2.9) inserted); to appear in Class. Quant. Grav
An apprach to generate large and small leptonic mixing angles
We take up the point of view that Yukawa couplings can be either 0 or 1, and
the mass patterns of fermions are generated purely from the structure of the
Yukawa matrices. We utilize such neutrino as well as charged leptonic textures
which lead to (maximal) mixing angles of in each sector for relevant
transitions. The combined leptonic CKM mixing angles are
which lead to very small relevant to solar neutrino and LSND
experiments. We propose that on the other hand the absence of the charged
leptonic partner of the sterile neutrino maintains the angle from the
neutrino sector for the transition and hence
atmospheric neutrino anomaly is explained through maximal mixing
A fast Monte Carlo algorithm for site or bond percolation
We describe in detail a new and highly efficient algorithm for studying site
or bond percolation on any lattice. The algorithm can measure an observable
quantity in a percolation system for all values of the site or bond occupation
probability from zero to one in an amount of time which scales linearly with
the size of the system. We demonstrate our algorithm by using it to investigate
a number of issues in percolation theory, including the position of the
percolation transition for site percolation on the square lattice, the
stretched exponential behavior of spanning probabilities away from the critical
point, and the size of the giant component for site percolation on random
graphs.Comment: 17 pages, 13 figures. Corrections and some additional material in
this version. Accompanying material can be found on the web at
http://www.santafe.edu/~mark/percolation
Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing
We use the canonical formalism developed together with David Robinson to st=
udy the Einstein equations on a null surface. Coordinate and gauge conditions =
are introduced to fix the triad and the coordinates on the null surface. Toget=
her with the previously found constraints, these form a sufficient number of
second class constraints so that the phase space is reduced to one pair of
canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to
both the Bondi-Sachs and the Newman-Penrose methods of studying the
gravitational field at null infinity. Asymptotic solutions in the vicinity of
null infinity which exclude logarithmic behavior require the connection to fall
off like after the Minkowski limit. This, of course, gives the previous
results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off
more slowly leads to logarithmic behavior which leaves null infinity intact,
allows for meaningful gravitational radiation, but the peeling theorem does not
extend to in the terminology of Newman-Penrose. The conclusions are in
agreement with those of Chrusciel, MacCallum, and Singleton. This work was
begun as a preliminary study of a reduced phase space for quantization of
general relativity.Comment: magnification set; pagination improved; 20 pages, plain te
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