24,434 research outputs found
Perfect Lattice Actions with and without Chiral Symmetry
We use perturbation theory to construct perfect lattice actions for fermions
and gauge fields by blocking directly from the continuum. When one uses a
renormalization group transformation that preserves chiral symmetry the
resulting lattice action for massless fermions is chirally symmetric but
nonlocal. When the renormalization group transformation breaks chiral symmetry,
the lattice action becomes local but chiral symmetry is explicitly broken. In
particular, starting with a chiral gauge theory in the continuum one either
obtains a lattice theory which is gauge invariant but nonlocal, or a local
theory with explicitly broken gauge invariance. In both cases the spectrum of
the lattice theory is identical with the one of the continuum and the anomaly
is correctly reproduced. We also apply our techniques to vector-like theories.
In particular we propose a new renormalization group transformation for QCD and
we optimize its parameters for locality of the perfect action.Comment: LaTex, 8 pages, Contribution to Lattice 95; Some minor typing errors
are correcte
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations
General relativistic corrections to the expansion rate of the Universe arise
when the Einstein equations are averaged over a spatial volume in a locally
inhomogeneous cosmology. It has been suggested that they may contribute to the
observed cosmic acceleration. In this paper, we propose a new scheme that
utilizes numerical simulations to make a realistic estimate of the magnitude of
these corrections for general inhomogeneities in (3+1) spacetime. We then
quantitatively calculate the volume averaged expansion rate using N-body
large-scale structure simulations and compare it with the expansion rate in a
standard FRW cosmology. We find that in the weak gravitational field limit, the
converged corrections are slightly larger than the previous claimed 10^{-5}
level, but not large enough nor even of the correct sign to drive the current
cosmic acceleration. Nevertheless, the question of whether the cumulative
effect can significantly change the expansion history of the Universe needs to
be further investigated with strong-field relativity.Comment: 13 pages, 6 figures, improved version published in Phys. Rev.
Quantum affine Toda solitons
We review some of the progress in affine Toda field theories in recent years,
explain why known dualities cannot easily be extended, and make some
suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision
A Lorentz-Poincar\'e type interpretation of the Weak Equivalence Principle
The validity of the Weak Equivalence Principle relative to a local inertial
frame is detailed in a scalar-vector gravitation model with Lorentz-Poincar\'e
type interpretation. Given the previously established first Post-Newtonian
concordance of dynamics with General Relativity, the principle is to this order
compatible with GRT. The gravitationally modified Lorentz transformations, on
which the observations in physical coordinates depend, are shown to provide a
physical interpretation of \emph{parallel transport}. A development of
``geodesic'' deviation in terms of the present model is given as well.Comment: v1: 9 pages, 2 figures, v2: version to appear in International
Journal of Theoretical Physic
A Perturbative Construction of Lattice Chiral Fermions
We perform a renormalization group transformation to construct a lattice
theory of chiral fermions. The field variables of the continuum theory are
averaged over hypercubes to define lattice fields. Integrating out the
continuum variables in perturbation theory we derive a chirally invariant
effective action for the lattice fields. This is consistent with the
Nielsen-Niniomiya theorem because the effective action is nonlocal. We also
construct the axial current on the lattice and we show that the axial anomaly
of the continuum theory is reproduced in the Schwinger model. This shows that
chiral fermions can be regularized on the lattice.Comment: 8 pages, LaTe
Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
We propose a method to obtain an improved Hamiltonian (action) for the Ising
universality class in three dimensions. The improved Hamiltonian has suppressed
leading corrections to scaling. It is obtained by tuning models with two
coupling constants. We studied three different models: the +1,-1 Ising model
with nearest neighbour and body diagonal interaction, the spin-1 model with
states 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the
lattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling
properties of the suitably tuned spin-1 model are compared in detail with those
of the standard Ising model. Great care is taken to estimate the systematic
errors from residual corrections to scaling. Our best estimates for the
critical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error
estimates take into account the statistical and systematic uncertainties.Comment: 55 pages, 12 figure
Perfect Lattice Actions for Staggered Fermions
We construct a perfect lattice action for staggered fermions by blocking from
the continuum. The locality, spectrum and pressure of such perfect staggered
fermions are discussed. We also derive a consistent fixed point action for free
gauge fields and discuss its locality as well as the resulting static
quark-antiquark potential. This provides a basis for the construction of
(classically) perfect lattice actions for QCD using staggered fermions.Comment: 30 pages, LaTex, 10 figure
Evolution with hole doping of the electronic excitation spectrum in the cuprate superconductors
The recent scanning tunnelling results of Alldredge et al on Bi-2212 and of
Hanaguri et al on Na-CCOC are examined from the perspective of the BCS/BEC
boson-fermion resonant crossover model for the mixed-valent HTSC cuprates. The
model specifies the two energy scales controlling the development of HTSC
behaviour and the dichotomy often now alluded to between nodal and antinodal
phenomena in the HTSC cuprates. Indication is extracted from the data as to how
the choice of the particular HTSC system sees these two basic energy scales
(cursive-U, the local pair binding energy and, Delta-sc, the nodal BCS-like gap
parameter) evolve with doping and change in degree of metallization of the
structurally and electronically perturbed mixed-valent environment.Comment: 19 pages, 5 figure
More on the infrared renormalization group limit cycle in QCD
We present a detailed study of the recently conjectured infrared
renormalization group limit cycle in QCD using chiral effective field theory.
It was conjectured that small increases in the up and down quark masses can
move QCD to the critical trajectory for an infrared limit cycle in the
three-nucleon system. At the critical quark masses, the binding energies of the
deuteron and its spin-singlet partner are tuned to zero and the triton has
infinitely many excited states with an accumulation point at the three-nucleon
threshold. We exemplify three parameter sets where this effect occurs at
next-to-leading order in the chiral counting. For one of them, we study the
structure of the three-nucleon system in detail using both chiral and contact
effective field theories. Furthermore, we investigate the matching of the
chiral and contact theories in the critical region and calculate the influence
of the limit cycle on three-nucleon scattering observables.Comment: 17 pages, 7 figures, discussion improved, results unchanged, version
to appear in EPJ
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