Abstract:
Excited negative parity hyperon masses are calculated in a chiral bag model in which the pion and the kaon fields are treated as perturbations. We also calculate the hadronic widths of $\lama$ and $\lamb$ as well as the coupling constants of the lightest $I=0$ excited hyperon to the meson-baryon channels, and discuss how the dispersive effects of the hadronic meson-baryon decay channels affect the excited hyperon masses. Meson cloud corrections to the electromagnetic decay widths of the two lightest excited hyperons into ground states $\lamz$ and $\sigz$ are calculated within the same model and are found to be small. Our results strengthen the argument that predictions of these hyperon radiative decay widths provide an excellent test for various quark models of hadrons.

Abstract:
Relativistic exchange current corrections to the impulse approximation in low and intermediate energy neutrino--nucleus scattering are presented assuming non--vanishing strange quark form factors for constituent nucleons. Two--body exchange current operators which treat {\em all} $SU(3)$ vector and axial currents on an equal footing are constructed by generalizing the soft--pion dominance method of Chemtob and Rho. For charged current reactions, exchange current corrections can reduce the impulse approximation results by 5 to 10 \% depending on the nuclear density. A finite strange quark form factor may change the total cross section for neutral current scattering by 20\% while exchange current corrections are found to be sensitive to the nuclear density. Implications on the current LSND experiment to extract the strange quark axial form factor of the nucleon are discussed.

Abstract:
In this two part series a chiral confining model of baryons is used to describe low--lying negative parity resonances $N^*$, $\Delta^*$, $\Lambda^*$ and $\Sigma^*$ in the mean field approximation. A physical baryon in this model consists of interacting valence quarks, mesons and a color and chiral singlet hybrid field coexisting inside a dynamically generated confining region. This first paper presents the quark contribution to the masses and wave functions of negative parity baryons calculated with an effective spin--isospin dependent instanton induced interaction. It does not include meson exchanges between quarks. The three--quark wave functions are used to calculate meson--excited baryon vertex functions to lowest order in meson--quark coupling. When the baryons are on mass--shell each of these vertex functions is a product of a coupling constant and a form factor. As examples, quark contributions to $N^*$ hadronic form factors as well as axial coupling constants are extracted from the vertex functions and problems with the analytical behaviour of the model form factors are discussed. The second paper will examine the mesonic corrections to excited baryon properties in the heavy baryon and one--loop approximations.

Abstract:
Relativistic exchange current corrections to neutrino--nucleus cross sections are presented assuming non--vanishing strange quark form factors for the constituent nucleons. For charged current processes the exchange current corrections can lower the impulse approximation results by 10\% while these corrections are found to be sensitive to both the nuclear density and the strange quark axial form factor of the nucleon for neutral current processes. Implications on the LSND experiment to determine this form factor are discussed.

Abstract:
We study the critical behavior of lattice Quantum Chromodynamics (QCD) in the strong coupling approximation with Kogut-Susskind and Wilson fermions at finite temperature ($T$) and zero chemical potential. Using the Hamiltonian formulation we construct a mean field solution to the equation of motion at finite $T$ and use it to study the elementary thermal excitations and to extract some critical exponents characterizing the observed second order phase transition. We find similar critical behaviors for Kogut-Susskind and Wilson fermions at finite $T$

Abstract:
We construct a solution to the equation of motion of Hamiltonian lattice QCD in the strong coupling limit using Wilson fermions which exactly diagonalizes the Hamiltonian to second order in the field operators. This solution obeys the free lattice Dirac equation with a dynamical mass which is identified with the gap. The equation determining this gap is derived and it is found that the dynamical quark mass is a constant to lowest order in N_c but becomes momentum dependent once 1/N_c corrections are taken into account. We interpret our solution within the framework of the N-quantum approach to quantum field theory and discuss how our formalism may be systematically extended to study bound states at finite temperature and chemical potential.

Abstract:
The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. Our result is in qualitative agreement with continuum models and should be verifiable by future lattice simulations of strongly coupled QCD at finite density.

Abstract:
Using an effective strongly coupled lattice QCD Hamiltonian and Wilson fermions we calculate the equation of state for cold and dense quark matter by constructing an ansatz which exactly diagonalizes the Hamiltonian to second order in field operators for all densities. This ansatz obeys the free lattice Dirac equation with a chemical potential term and a mass term which is interpreted as the dynamical quark mass. We find that the order of chiral phase transition depends on the values of input parameters. In the phase with spontaneously broken chiral symmetry the quark Fermi sea has negative pressure indicating its mechanical instability. This result is in qualitative agreement with those obtained using continuum field theory models with four--point interactions.

Abstract:
We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian using Wilson fermions. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. This result is in qualitative agreement with continuum models and should be verifiable by future numerical simulations.

Abstract:
We extend the N-quantum approach to quantum field theory to finite temperature ($T$) and chemical potential ($\mu$) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2)$_{rm f}$ $otimes$ SU(3)$_{\rm c}$ version of the model can lead to a lowering of the vacuum energy density. We discuss how to go beyond the mean field approximation by including higher order terms in the Haag expansion.