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

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

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

Flavor Changing Scalar Interactions

The smallness of fermion masses and mixing angles has recently been been attributed to approximate global $U(1)$ symmetries, one for each fermion type. The parameters associated with these symmetry breakings are estimated here directly from observed masses and mixing angles. It turns out that although flavor changing reaction rates may be acceptably small in electroweak theories with several scalar doublets without imposing any special symmetries on the scalars themselves, such theories generically yield too much CP violation in the neutral kaon mass matrix. Hence in these theories CP must also be a good approximate symmetry. Such models provide an alternative mechanism for CP violation and have various interesting phenomenological features.Comment: 18 pages. UTTG-22-92; LBL 33016; UCB 92/3

Light-cone QCD predictions for elastic ed-scattering in the intermediate energy region

The contributions of helicity-flip matrix elements to the deuteron form factors are discussed in the light-cone frame. Normalized $A(Q^2)$, $B(Q^2)$, $G_Q(Q^2)$ and $T_{20}$ are obtained in a simple QCD-inspired model. We find that $G_{+-}^+$ plays an important role in $G_Q(Q^2)$. Our numerical results are consistent with the data in the intermediate energy region.Comment: 9 pages, REVTeX file, 5 figure

Block-Spin Approach to Electron Correlations

We consider an expansion of the ground state wavefunction of quantum lattice many-body systems in a basis whose states are tensor products of block-spin wavefunctions. We demonstrate by applying the method to the antiferromagnetic spin-1/2 chain that by selecting the most important many-body states the technique affords a severe truncation of the Hilbert space while maintaining high accuracy.Comment: 17 pages, 3 Postscript figure

Introduction to light cone field theory and high energy scattering

In this set of four lectures, we provide an elementary introduction to light cone field theory and some of its applications in high energy scattering.Comment: 28 pages, LaTeX, invited lectures at Cape Town summer school in theoretical physic

CORE Technology and Exact Hamiltonian Real-Space Renormalization Group Transformations

The COntractor REnormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is presented. The method defines a systematic and nonperturbative means of implementing Kadanoff-Wilson real-space renormalization group transformations using cluster expansion and contraction techniques. We illustrate the approach and demonstrate its effectiveness using scalar field theory, the Heisenberg antiferromagnetic chain, and the anisotropic Ising chain. Future applications to the Hubbard and t-J models and lattice gauge theory are discussed.Comment: 65 pages, 9 Postscript figures, uses epsf.st

Compact QED3_3 - a simple example of a variational calculation in a gauge theory

We apply a simple mean field like variational calculation to compact QED in 2+1 dimensions. Our variational ansatz explicitly preserves compact gauge invariance of the theory. We reproduce in this framework all the known results, including dynamical mass generation, Polyakov scaling and the nonzero string tension. It is hoped that this simple example can be a useful reference point for applying similar approximation techniques to nonabelian gauge theories.Comment: 18 pages, OUTP- 94-23 P, TPI-MINN-94/37-

Forward-Backward Asymmetries in Hadronically Produced Lepton Pairs

It has now become possible to observe appreciable numbers of hadronically produced lepton pairs in mass ranges where the contributions of the photon and $Z^0$ are comparable. Consequently, in the reaction $p \bar p \to \ell^- \ell^+ + \ldots$, substantial forward-backward asymmetries can be seen. These asymmetries provide a test of the electroweak theory in a new regime of energies, and can serve as diagnostics for any new neutral vector bosons coupling both to quarks and to charged lepton pairs.Comment: 11 pages, latex, 4 uuencoded figures sent separately, Fig. 2 revise