We study the four-quark interaction as a first step in understanding the QCD origin of the nuclear force in nature. We simulate QCD on a 20 x 20 x 20 x 32 space-time lattice with the simplifying quenched and static approximations, and with the SU(2) gauge group. Recent four-quark simulations reveal interesting tetrahedral geometry and planar four-quark flux distributions that cannot be explained by existing models. We simulate the flux distribution for the still-unexplored next higher level of geometrical complexity, namely four quarks on the corners of a tetrahedron. In order to complete the simulation within the allotted computing time, we have improved the approach used to simulate the flux distribution. Compared to previous approaches, the new approach nearly eliminates the bottleneck of the computing time, provides more than a 100-time speedup in our project, and also provides a better strategy for improving signal-noise ratio and suppressing signal distortion from the lattice structure. As the result of this improved approach, we have observed the long diagonal flux tube structure, repeated the Helsinki group's 1998 results for the flux distribution of a square geometry, and, for the first time, simulated the flux distribution of a tetrahedron geometry. In this thesis, we also explore some fundamental questions of lattice QCD related to computability theory and complexity theory. / Graduation date: 2001

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We study a model for inclusive central particle production in pp and pp reactions based on parton model concepts and lowest-order QCD. In this picture, two-gluon fusion creates a heavy excited state (fireball) whose decay (described by statistical considerations) leads to the creation of light hadrons with low transverse momenta. Agreement with experimental data is found to be good. This first model is then embedded (providing energy dependence) in a two-component eikonal model used to study elastic diffraction and unifying parton model and impact parameter formulations. We discuss the inclusion of a real part for the elastic amplitude, the removal of multiple diffraction zeros and the behavior of this second model up to the multi-TeV energy range (the Froissart bound is not saturated). We find excellent agreement with a large body of experimental data.

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Two aspects of gauge theories are studied in the non-perturbative regime; firstly, using a set of pre-determined, approximate renormalised Feynman rules, the divergent parts of the O(α(_8)) virtual graphs of the process e(^+)e" → qq are determined to explicitly test whether multiplicative renormalisation is preserved by these rules. The calculation is performed using dimensional regularisation in 2(2 - ɛ) dimensional Euclidean space, where the divergences appear as 1/ɛ(^n) poles as ɛ → 0 Though the corrections to both the fermion-photon vertex and to the final state self energy are shown to have 1/ɛ singularities, the coefficients of these are quite different. This mis-match in singular behaviour signals the breakdown of multiplicative renormalisation, which, in turn, implies that the physical process is not guaranteed to be finite and the rules used are in admissable as a set of consistent Feynman rules. The second investigation is to solve numerically the Schwinger-Dyson equation for the fermion propagator in QED in three (Euclidean) dimensions. The aim being to study the scale of dynamical mass generation. To control infrared divergences the 1/N (flavour) expansion is used and to close the equation vertex and gauge propagator are approximated by their lowest order forms in 1/N. Numerical solutions for the fermion self energy and wavefunction renormalisation are determined. The latter is found not to be suppressed by O(1/N), contrary to the expectation of Appelquist et al, and the coupled equation for these functions has to be solved. It is then found that a mass scale is dynamically generated and that a scale hierarchy between it and the dimensionful coupling, α, of many orders of magnitude exists (typically m/a ~ 10(^-7) for N(_F)=5). Thus showing, albeit in a simplified 'toy' model, how large scale hierarchies can 'naturally' occur in gauge theories with spontaneously broken symmetries.

We analyze the hadronic phase of QCD using effective thermal field theory techniques. Our goal is to investigate the medium created in heavy ion collisions by calculating the electromagnetic emissivity of strongly interacting matter in the hadronic phase. We proceed through examining the vector meson properties in a thermal bath where the temperature reaches deconfinement and chiral symmetry is restored. In particular we observe the behavior of the rho spectral function in thermal medium and use it as a probe to examine the thermal environment generated in the collision.

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Thesis supervisor: William H. Klink. Includes bibliographic references (p. 71).