11,702 research outputs found
Solutions of the Ginsparg-Wilson Relation
We analyze general solutions of the Ginsparg-Wilson relation for lattice
Dirac operators and formulate a necessary condition for such operators to have
non-zero index in the topologically nontrivial background gauge fields.Comment: 6 pages, latex, no figures, set T to 1 in eqs. (10)--(13
Ginsparg-Wilson Relation and Ultralocality
It is shown that it is impossible to construct a free theory of fermions on
infinite hypercubic Euclidean lattice in four dimensions that is: (a)
ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding
kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation),
(d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change
Low energy scattering with a nontrivial pion
An earlier calculation in a generalized linear sigma model showed that the
well-known current algebra formula for low energy pion pion scattering held
even though the massless Nambu Goldstone pion contained a small admixture of a
two-quark two-antiquark field. Here we turn on the pion mass and note that the
current algebra formula no longer holds exactly. We discuss this small
deviation and also study the effects of an SU(3) symmetric quark mass type term
on the masses and mixings of the eight SU(3) multiplets in the model. We
calculate the s wave scattering lengths, including the beyond current algebra
theorem corrections due to the scalar mesons, and observe that the model can
fit the data well. In the process, we uncover the way in which linear sigma
models give controlled corrections (due to the presence of scalar mesons) to
the current algebra scattering formula. Such a feature is commonly thought to
exist only in the non-linear sigma model approach.Comment: 15 pages, 8 figure
Ginsparg-Wilson-Luscher Symmetry and Ultralocality
Important recent discoveries suggest that Ginsparg-Wilson-Luscher (GWL)
symmetry has analogous dynamical consequences for the theory on the lattice as
chiral symmetry does in the continuum. While it is well known that inherent
property of lattice chiral symmetry is fermion doubling, we show here that
inherent property of GWL symmetry is that the infinitesimal symmetry
transformation couples fermionic degrees of freedom at arbitrarily large
lattice distances (non-ultralocality). The consequences of this result for
ultralocality of symmetric actions are discussed.Comment: 18 pages, LATEX. For clarity changed to infinitesimal
transformations, typos corrected, explicit hypothesis adde
Electroweak Sudakov Corrections using Effective Field Theory
Electroweak Sudakov corrections of the form alpha^n log^m s/M_{W,Z}^2 are
summed using renormalization group evolution in soft-collinear effective theory
(SCET). Results are given for the scalar, vector and tensor form-factors for
fermion and scalar particles. The formalism for including massive gauge bosons
in SCET is developed.Comment: 5 page
Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime
The measurement of the lateral Casimir force between two aligned sinusoidally
corrugated Au-coated surfaces has been performed in the nonadditive regime. The
use of deeper corrugations also allowed to demonstrate an asymmetry in the
phase dependences of the lateral Casimir force, as predicted earlier. The
measurement data are found to be in excellent agreement with the exact
theoretical results computed at T=300 K including effect of real material
properties. The deviations between the exact theory and the proximity force
approximation are quantified. The obtained results are topical for applications
in nanomachines.Comment: 9 pages, 3 figure
Soft-Collinear Factorization and Zero-Bin Subtractions
We study the Sudakov form factor for a spontaneously broken gauge theory
using a (new) Delta -regulator. To be well-defined, the effective theory
requires zero-bin subtractions for the collinear sectors. The zero-bin
subtractions depend on the gauge boson mass M and are not scaleless. They have
both finite and 1/epsilon contributions, and are needed to give the correct
anomalous dimension and low-scale matching contributions. We also demonstrate
the necessity of zero-bin subtractions for soft-collinear factorization. We
find that after zero-bin subtractions the form factor is the sum of the
collinear contributions 'minus' a soft mass-mode contribution, in agreement
with a previous result of Idilbi and Mehen in QCD. This appears to conflict
with the method-of-regions approach, where one gets the sum of contributions
from different regions.Comment: 9 pages, 5 figures. V2:ref adde
A Quantum Anti-Zeno Paradox
We establish an exact differential equation for the operator describing
time-dependent measurements continuous in time and obtain a series solution.
Suppose the projection operator is measured
continuously from t = 0 to T, where E is a projector leaving the initial state
unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness
conditions in t. We prove that the probability of always finding E(t) = 1 from
t = 0 to T is unity. If , the watched kettle is sure to `boil'.Comment: 10 pages,late
Strong coupling between single-electron tunneling and nano-mechanical motion
Nanoscale resonators that oscillate at high frequencies are useful in many
measurement applications. We studied a high-quality mechanical resonator made
from a suspended carbon nanotube driven into motion by applying a periodic
radio frequency potential using a nearby antenna. Single-electron charge
fluctuations created periodic modulations of the mechanical resonance
frequency. A quality factor exceeding 10^5 allows the detection of a shift in
resonance frequency caused by the addition of a single-electron charge on the
nanotube. Additional evidence for the strong coupling of mechanical motion and
electron tunneling is provided by an energy transfer to the electrons causing
mechanical damping and unusual nonlinear behavior. We also discovered that a
direct current through the nanotube spontaneously drives the mechanical
resonator, exerting a force that is coherent with the high-frequency resonant
mechanical motion.Comment: Main text 12 pages, 4 Figures, Supplement 13 pages, 6 Figure
Contribution of the massive photon decay channel to neutrino cooling of neutron stars
We consider massive photon decay reactions via intermediate states of
electron-electron-holes and proton-proton-holes into neutrino-antineutrino
pairs in the course of neutron star cooling. These reactions may become
operative in hot neutron stars in the region of proton pairing where the photon
due to the Higgs-Meissner effect acquires an effective mass that
is small compared to the corresponding plasma frequency. The contribution of
these reactions to neutrino emissivity is calculated; it varies with the
temperature and the photon mass as
for . Estimates show that these processes appear as extra
efficient cooling channels of neutron stars at temperatures K.Comment: accepted to publication in Zh. Eksp. Teor. Fiz. (JETP
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