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This is the final report on grant DE-FG05-96ER40979 from the US 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). 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 ({approx} 1 GeV), the coupling constant in QCD is large, preventing application of the physicist's usual tool, perturbation theory. Non-perturbative 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. A major research topic was the study of improved lattice actions, designed to diminish finite lattice spacing effects and thus accelerate the approach to the continuum limit. Most of this work was carried out in the quenched approximation. Very encouraging results were obtained. In the second half of the funding period, a major focus of the group has been the use of a new lattice fermion representation, Overlap fermions, that has achieved the much desired goal of preserving the chiral symmetry properties of the continuum theory at finite lattice spacing. After developing an algorithm for the numerical simulations of overlap fermions, the SCRI group has completed the first studies of the relation between chiral symmetry breaking and topology using this new formalism

Final report to the DOE for the period 8/1/96 to 5/31/00 by the SCRI Theoretical High Energy Group