Browsing by Author "Mattingly, Alan Charles"

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    The quark-Skyrme nucleon
    (1990) Mattingly, Alan Charles; Duck, Ian M.
    We construct a quark-soliton model of the nucleon which interpolates between the MIT bag model of arbitrarily confined relativistic quarks and the Skyrme model in which the nucleon is a topological knot in the pion field. Confinement is achieved using the color dielectric model. The field equations are solved numerically for the so called hedgehog state for which the field equations reduce to radial ones. Nucleon observables are calculated by projecting the quark-soliton hedgehog ground state onto spin-isospin eigenstates, which are taken to be variationally best nucleon and nucleon isobar states.
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    'Variational' optimization in quantum field theory
    (1993) Mattingly, Alan Charles; Stevenson, Paul M.
    We examine two different techniques for studying quantum field theories in which a 'variational' optimization of parameters plays a crucial role. In the context of the O(N)-symmetric $\lambda\phi\sp4$ theory we discuss variational calculations of the effective potential that go beyond the Gaussian approximation. Trial wavefunctionals are constructed by applying a unitary operator $U = e\sp{-is\pi\sb{R}\phi\sbsp{T}{2}}$ to a Gaussian state. We calculate the expectation value of the Hamiltonian using the non-Gaussian trial states generated, and thus obtain optimization equations for the variational-parameter functions of the ansatz. At the origin, $\varphi\sb{c} = 0,$ these equations can be solved explicitly and lead to a nontrivial correction to the mass renormalization, with respect to the Gaussian case. Numerical results are obtained for the (0 + 1)-dimensional case and show a worthwhile quantitative improvement over the Gaussian approximation. We also discuss the use of optimized perturbation theory (OPT) as applied to the third-order quantum chromodynamics (QCD) corrections to $R\sb{e\sp+e\sp-}.$ The OPT method, based on the principle of minimal sensitivity, finds an effective coupling constant that remains finite down to zero energy. This allows us to apply the Poggio-Quinn-Weinberg smearing method down to energies below 1 GeV, where we find good agreement between theory and experiment. The couplant freezes to a zero-energy value of $\alpha\sb{s}/\pi = 0.26,$ which is in remarkable concordance with values obtained phenomenologically.