2,653 research outputs found
CORE and the Haldane Conjecture
The Contractor Renormalization group formalism (CORE) is a real-space
renormalization group method which is the Hamiltonian analogue of the Wilson
exact renormalization group equations. In an earlier paper\cite{QGAF} I showed
that the Contractor Renormalization group (CORE) method could be used to map a
theory of free quarks, and quarks interacting with gluons, into a generalized
frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to
study these theories. Since generalizations of HAF's exhibit all sorts of
subtle behavior which, from a continuum point of view, are related to
topological properties of the theory, it is important to know that CORE can be
used to extract this physics. In this paper I show that despite the folklore
which asserts that all real-space renormalization group schemes are necessarily
inaccurate, simple Contractor Renormalization group (CORE) computations can
give highly accurate results even if one only keeps a small number of states
per block and a few terms in the cluster expansion. In addition I argue that
even very simple CORE computations give a much better qualitative understanding
of the physics than naive renormalization group methods. In particular I show
that the simplest CORE computation yields a first principles understanding of
how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1
HAF.Comment: 36 pages, 4 figures, 5 tables, latex; extensive additions to conten
Form factors in quantum electrodynamics
The electromagnetic form factors of an electron in pure quantum electrodynamics are analyzed with the techniques of dispersion relations. The viewpoint is adopted here that no subtractions are required in the construction of dispersion relations for the electromagnetic vertex. This leads to coupled integral equations for the form factors in terms of other physical amplitudes; electron-positron scattering, for example. The relation between this and the usual perturbation approach to quantum electrodynamics, and the validity and consequences of the "no-subtraction" philosophy, are discussed
Status of Spin Physics - Experimental Summary
The current status of spin physics experiments, based on talks presented at
the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in
Beijing, 2001, is summarized in this article. Highlights of recent experimental
results at SLAC, JLab, and DESY, as well as future plans at these facilities
and at RHIC-spin are discussed.Comment: 18 pages, 7 figures, Invited talk presented at the Third
Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing,
October, 200
Wide-angle pair production and quantum electrodynamics at small distances
Wide-angle photoproduction of high-energy electron-positron pairs in hydrogen is proposed and analyzed as a test of quantum electrodynamics at distances ≤10^-13 cm. The effect of proton structure can be removed in terms of the two form factors measured in the elastic electron-proton scattering process. Cross sections are presented for two classes of pair production experiments: (1) those detecting one of the final particles, and (2) coincidence experiments. In addition to kinematic, anomalous moment, and nucleon form-factor corrections to the Bethe-Heitler formula, dynamical corrections to the proton current and radiative corrections are calculated. The final theoretical formula is believed to be accurate to 2%. A simple cutoff model suggests that a 5% accuracy in an experiment of type (1) tests the electron propagator at distances ∼0.7×10^-13 cm, while a 10% accuracy in a coincidence arrangement of type (2) probes the electron propagator at ∼0.3×10^-13 cm
Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders
Threshold enhanced perturbative QCD corrections to rapidity distributions of
and bosons at hadron colliders are presented using the Sudakov
resummed cross sections at NLO level. We have used renormalisation group
invariance and the mass factorisation theorem that these hard scattering cross
sections satisfy to construct the QCD amplitudes. We show that these higher
order threshold QCD corrections stabilise the theoretical predictions for
vector boson production at the LHC under variations of both renormalisation and
factorisation scales.Comment: 17 pages, 8 eps figures. This paper is dedicated to the memory of
W.L.G.A.M. van Neerve
Is the ground state of Yang-Mills theory Coulombic?
We study trial states modelling the heavy quark-antiquark ground state in
SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a
thin string of glue is found to be a poor description of the continuum ground
state; the infinitesimal thickness of the string leads to UV artifacts which
suppress the overlap with the ground state. Contrastingly, a state which
surrounds the quarks with non-abelian Coulomb fields is found to have a good
overlap with the ground state for all charge separations. In fact, the overlap
increases as the lattice regulator is removed. This opens up the possibility
that the Coulomb state is the true ground state in the continuum limit.Comment: 10 pages, 9 .eps figure
The Nucleon Spin Polarizability at Order ) in Chiral Perturbation Theory
We calculate the forward spin-dependent photon-nucleon Compton amplitude as a
function of photon energy at the next-to-leading () order in
chiral perturbation theory, from which we extract the contribution to nucleon
spin polarizability. The result shows a large correction to the leading order
contribution.Comment: 7 pages, latex, 2 figures included as .eps file
High-energy limit of form factors
This theorem is proved: For finite charge renormalization constant Z3-1, the form factors describing any vertex with two particles on the mass shell must vanish at infinite momentum transfer. The relation of this result to the work of Lehmann, Symanzik, and Zimmermann is discussed
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