8,896 research outputs found
Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation
We propose a new method to characterize the different phases observed in the
non-perturbative numerical approach to quantum gravity known as Causal
Dynamical Triangulation. The method is based on the analysis of the eigenvalues
and the eigenvectors of the Laplace-Beltrami operator computed on the
triangulations: it generalizes previous works based on the analysis of
diffusive processes and proves capable of providing more detailed information
on the geometric properties of the triangulations. In particular, we apply the
method to the analysis of spatial slices, showing that the different phases can
be characterized by a new order parameter related to the presence or absence of
a gap in the spectrum of the Laplace-Beltrami operator, and deriving an
effective dimensionality of the slices at the different scales. We also propose
quantities derived from the spectrum that could be used to monitor the running
to the continuum limit around a suitable critical point in the phase diagram,
if any is found.Comment: 21 pages, 26 figures, 2 table
Feynman rules for Gauss's law
I work on a set of Feynman rules that were derived in order to incorporate
the constraint of Gauss's law in the perturbation expansion of gauge field
theories and calculate the interaction energy of two static sources. The
constraint is implemented via a Lagrange multiplier field, , which, in
the case of the non-Abelian theory, develops a radiatively generated effective
potential term. After analysing the contributions of various solutions for
, the confining properties and the various phases of the theory are
discussed.Comment: 18 pages, 10 figure
Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations
provided, figure and references added, published versio
Center vortices as rigid strings
It is shown that the action associated with center vortices in SU(2) lattice
gauge theory is strongly correlated with extrinsic and internal curvatures of
the vortex surface and that this correlation persists in the continuum limit.
Thus a good approximation for the effective vortex action is the action of
rigid strings, which can reproduce some of the observed geometric properties of
center vortices. It is conjectured that rigidity may be induced by some fields
localized on vortices, and a model-independent test of localization is
performed. Monopoles detected in the Abelian projection are discussed as
natural candidates for such two-dimensional fields.Comment: 7 pages, 8 figures, RevTeX
Geometry of percolating monopole clusters
We perform detailed measurements of the geometrical characteristics of the
percolating cluster of the magnetic monopole currents in the confining phase of
the lattice SU(2) gluodynamics. The Maximal Abelian projection is used to
define the monopoles. The use of the geometrical language is motivated by
recent observations that the full non-Abelian action associated with the
monopoles corresponds to point-like particles on the currently available
lattices. Scaling behavior of various quantities is observed.Comment: 3 pages, 4 figures, Lattice2002(topology
Hadron Deformation and Form Factors from Lattice QCD
We review the current status of lattice QCD studies of the nucleon system. In
particular, we focus on the determination of the shape of the nucleon by
probing its wave function as well as by evaluating the N to Delta transition
form factors.Comment: 14 pages, 8 figures. Talk presented at the Workshop "The Shape of
Hadrons", Athens, Greece, 27-30 April 200
Universality of Mixed Action Extrapolation Formulae
Mixed action theories with chirally symmetric valence fermions exhibit very
desirable features both at the level of the lattice calculations as well as in
the construction and implementation of the low energy mixed action effective
field theory. In this work we show that when such a mixed action effective
field theory is projected onto the valence sector, both the Lagrangian and the
extrapolation formulae become universal in form through next to leading order,
for all variants of discretization methods used for the sea fermions. Our
conclusion relies on the chiral nature of the valence quarks. The result
implies that for all sea quark methods which are in the same universality class
as QCD, the numerical values of the physical coefficients in the various mixed
action chiral Lagrangians will be the same up to lattice spacing dependent
corrections. This allows us to construct a prescription to determine the mixed
action extrapolation formulae for a large class of hadronic correlation
functions computed in partially quenched chiral perturbation theory at the
one-loop level. For specific examples, we apply this prescription to the
nucleon twist--2 matrix elements and the nucleon--nucleon system. In addition,
we determine the mixed action extrapolation formula for the neutron EDM as this
provides a nice example of a theta-dependent observable; these observables are
exceptions to our prescription.Comment: 36 pages, appendix on twisted mass sea fermions added, expanded
discussion of NLO operators, version published in JHEP; typographical errors
corrected in Eqs. (68) and (69
Iterative Universal Rigidity
A bar framework determined by a finite graph and configuration in
space is universally rigid if it is rigid in any . We provide a characterization of universally rigidity for any
graph and any configuration in terms of a sequence of affine
subsets of the space of configurations. This corresponds to a facial reduction
process for closed finite dimensional convex cones.Comment: 41 pages, 12 figure
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