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

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

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

Final state interaction corrections to inelastic nucleon-nucleon scattering

The final state interaction corrections to the peripheral model calculation of Drell and Hiida of the process n + n → n + n + π are calculated. Methods of calculation and comparison with experiment are discussed. © 1963

Probing New Physics From CP Violation in Radiative B Decays

When new CP-violating interactions are dominated by flavor changing neutral particle exchanges, that may occur in many extensions of the standard model. We examine a type 3 two Higgs doublet model and find that direct CP asymmetries can be as large as about 25% . Time-dependent and time-integrated mixing-induced CP asymmetries up to 85 and 40 %, respectively, are possible without conflict with other constraints. It mainly requirs an enhanced chromo-magnetic dipole $b\to sg$ decay to be close to the present experimental bound.Comment: 7 pages, latex, no figure

Low mass lepton pair production in hadron collisions

The hadroproduction of lepton pairs with mass $Q$ and transverse momentum $Q_T$ can be described in perturbative QCD by the same partonic subprocesses as prompt photon production. We demonstrate that, like prompt photon production, lepton pair production is dominated by quark-gluon scattering in the region $Q_T>Q/2$. This leads to sensitivity to the gluon density in kinematical regimes that are accessible both at collider and fixed target experiments while eliminating the theoretical and experimental uncertainties present in prompt photon production.Comment: Talk given by M. Klasen at the International Conference on the Structure and Interactions of the Photon, PHOTON 99, Freiburg i. Brsg., Germany, May 23-27, 1999. To be published in the proceedings. 6 pages, 6 postscript figure

Model independent properties of two-photon exchange in elastic electron proton scattering

We derive from first principles, as the C-invariance of the electromagnetic interaction and the crossing symmetry, the general properties of two-photon exchange in electron-proton elastic scattering. We show that the presence of this mechanism destroys the linearity of the Rosenbluth separation.Comment: 12 pages, no figures- Corrected misprints, changes in P. 7. No changes in conclusion

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

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure