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

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

Dirac-Coulomb scattering with plane wave energy eigenspinors on de Sitter expanding universe

The lowest order contribution of the amplitude of Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given energy and helicity. We find that the total energy is conserved in the scattering process.Comment: 9 pages, no figure

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

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

The free Dirac spinors of the spin basis on the de Sitter expanding universe

It is shown that on the de Sitter space-time the global behavior of the free Dirac spinors in momentum representation is determined by several phases factors which are functions of momentum with special properties. Such suitable phase functions can be chosen for writing down the free Dirac quantum modes of the spin basis that are well-defined even for the particles at rest in the moving local charts where the modes of the helicity basis remain undefined. Under quantization these modes lead to a basis in which the one-particle operators keep their usual forms apart from the energy operator which lays out a specific term which depend on the concrete phase function one uses.Comment: 8 pages no figure

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 $Z$ and $W^\pm$ bosons at hadron colliders are presented using the Sudakov resummed cross sections at N${}^3$LO 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

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

Type Ia Supernovae, Evolution, and the Cosmological Constant

We explore the possible role of evolution in the analysis of data on SNe Ia at cosmological distances. First, using a variety of simple sleuthing techniques, we find evidence that the properties of the high and low redshift SNe Ia observed so far differ from one another. Next, we examine the effects of including simple phenomenological models for evolution in the analysis. The result is that cosmological models and evolution are highly degenerate with one another, so that the incorporation of even very simple models for evolution makes it virtually impossible to pin down the values of $\Omega_M$ and $\Omega_\Lambda$, the density parameters for nonrelativistic matter and for the cosmological constant, respectively. Moreover, we show that if SNe Ia evolve with time, but evolution is neglected in analyzing data, then, given enough SNe Ia, the analysis hones in on values of $\Omega_M$ and $\Omega_\Lambda$ which are incorrect. Using Bayesian methods, we show that the probability that the cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia data when one accounts for the possibility of evolution, provided that we do not discriminate among open, closed and flat cosmologies a priori. The case for nonzero cosmological constant is stronger if the Universe is presumed to be flat, but still depends sensitively on the degree to which the peak luminosities of SNe Ia evolve as a function of redshift. The estimated value of $H_0$, however, is only negligibly affected by accounting for possible evolution.Comment: 45 pages, 15 figures; accepted for publication in The Astrophysical Journal. Minor revisions and clarifications made including addition of recent reference