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Executive SummaryThis is the final report on grant DE-FG05-92ER40742 from the U S . Department of Energy supporting the research of the Theoretical High Energy Physics group at the Supercomputer Computations Research Institute (SCRI) at Florida State University. The research primarily involved lattice field theory simulations such as Quantum Chromodynamics (QCD) and the Standard Model of electroweak interactions. Although QCD is generally accepted as the theory which describes the strong interactions responsible for nuclear binding, convincing computations of the properties of the elementary particles from first principles are still elusive. The problem lies in the fact that for data at the "low" energies involved (-1 GeV), the coupling constant in QCD is large, preventing application of the physicist's usual tool, perturbation theory. Nonperturbative computations are necessary and they appear possible only via large scale numerical simulations. Especially simulations of "full QCD" , including the effect of light dynamical quarks, are extremely CPU time consuming. The scientists in SCRI's lattice gauge theory group have been in the forefront of such numerical simulations since the inception of SCRI in 1985.SCRI scientists have developed highly efficient algorithms and codes, which are fairly easily portable to various supercomputers, as well as workstations (used mainly for code development). In some cases the most frequently used code segments have been hand optimized for a particular computer architecture. With these codes they have performed numerical simulations of many interesting physics problems. Most of these computations were carried out on the CM-2 a t SCRI.Among the works completed by the members of the lattice group and their outside collaborators in QCD simulations are extensive hadronic spectrum computations with both Wilson and staggered fermions, and calculations of hadronic matrix elements and wavefunctions. Studies of the QCD p function with two flavors of Wilson fermions, and the study of a possible flavor-parity breaking phase in QCD with two flavors of Wilson fermions have been completed. Studies of the finite temperature behavior of QCD have also been a major activity within the group.Studies of non-relativistic QCD, both for heavy-heavy mesons and for the heavy quark in heavy-light mesons have been done. The latter resulted in a computation of the B meson spectrum and its decay constant.Combining large N analytic computations within the Higgs sector of the standard model and numerical simulations at N = 4 have yielded a computation of the upper bound of the mass of the Higgs particle, as well as the energy scale above which deviations from the Standard Model may be expected.A major research topic during the second half of the grant period was the study of improved lattice actions, designed to diminish finite lattice spacing effects and thus accel...