Hamiltonian lattice gauge theory: wavefunctions on large lattices

We discuss an algorithm for the approximate solution of Schrodinger's equation for lattice gauge theory, using lattice SU(3) as an example. A basis is generated by repeatedly applying an effective Hamiltonian to a ``starting state.'' The resulting basis has a cluster decomposition and long-range correlations. One such basis has about 10^4 states on a 10X10X10 lattice. The Hamiltonian matrix on the basis is sparse, and the elements can be calculated rapidly. The lowest eigenstates of the system are readily calculable.Comment: 4 pages, (contribution to Lattice'92 conference); requires espcrc2.st

A Gauge-fixed Hamiltonian for Lattice QCD

We study the gauge fixing of lattice QCD in 2+1 dimensions, in the Hamiltonian formulation. The technique easily generalizes to other theories and dimensions. The Hamiltonian is rewritten in terms of variables which are gauge invariant except under a single global transformation. This paper extends previous work, involving only pure gauge theories, to include matter fields.Comment: 7 pages of LaTeX, RU-92-45 and BUHEP-92-3

Regge Trajectories with Square-Root Branch Points and Their Regge Cuts

We discuss branch points in the complex angular momentum plane formed by two Regge poles on trajectories with square-root branch points at t=0. We find several new cuts which collide with the expected Mandelstam cuts at t=0. In the bootstrap of the Pomeranchon pole, the collection of cuts has the same effect as in the case of linear trajectories: The Pomeranchon can have α(0)=1 only if certain couplings vanish at t=0

Modified WKB approximation

In the WKB approximation the \nabla^2S term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the \nabla^2 S term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to \phi^4 field theory.In the WKB approximation the $\nabla~2S$ term in Schrodinger's equation is subordinate to the |\nabla S|~2 term. Here we study an anti-WKB approximation in which the $\nabla~2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi~4$ field theory.In the WKB approximation the $\nabla^2S$ term in Schrodinger's equation is subordinate to the |\nabla S|^2 term. Here we study an anti-WKB approximation in which the $\nabla^2 S$ term dominates (after a guess for S is supplied). Our approximation produces only the nodeless ground state wavefunction, but it can be used in potential problems where the potential is not symmetric, and in problems where there are many degrees of freedom. As a test, we apply the method to potential problems, including the hydrogen and helium atoms and to $\phi^4$ field theory

Synthesis and Characterization of Cobalt(II), Nickel(II) and Copper(II) Chloride Complexes with Bis[(diphenylphosphinyl)methyl] phenylphosphine Oxide and Bis[(diphenylphosphinyl)methyl]phosphinic Acid

A series of cobalt(II), nickel(II) and copper(II) chloride complexes with the tripode organophosphorous compounds: bis[(diphenylphosphinyl) methyl]phenylphosphine oxide (RPPh) and bis [(diphenylphosphinyl)methyl]phosphinic acid (RPOH) were studied. Complexes of the general stoichiometry [M(RPPh)s] [MC14] • 4H20 and fM(RPOH)Cl · nH20]m (M = Co(II), Ni(II) or Cu(II); n = 0 - 4, m = 1, 2 or more) were isolated. According to spectral and magnetic data, complexes with the RPPh ligand appear to have both an octahedral and a tetrahedral surrounding of the metal(II) ion. For the complexes [M(RPOH)Cl · nH20]m the electronic effect of the metal ion seems to be predominant. A tetrahedra<! surrounding for the cobalt(II) complex, an octahedral surrounding for the nickel(II) complex and a tetragonal distorted octahedral surrounding for the copper(II) complex has to be assumed