We present the calculational details omitted in Phys. Rev. D 53 (1996) 1416, along with discussion of intrinsic transverse momentum effects, higher-twist contributions, and the gauge-dependence of the resummation procedure.

We consider the revival properties of quantum systems with an eigenspectrum E_{n} ~ n^{2}, and compare them with the simplest member of this class - the infinite square well. In addition to having perfect revivals at integer multiples of the revival time t_{R}, these systems all enjoy perfect fractional revivals at quarterly intervals of t_{R}. A closer examination of the quantum evolution is performed for the Scarf potentials, and comparison is made with the infinite square well using quantum carpets.

We use the LEP/SLD data to place constraints on Topcolor Assisted Technicolor Models. We find that due to a large negative shift in R_b induced by charged top-pion exchange, it is difficult to make the models compatible with experiment.

We show that radiative corrections to the Higgs potential in supersymmetric theories with large tan beta generically lead to large differences in the light Higgs boson decay branching fractions compared to those of the standard model Higgs boson. In contrast, the light Higgs boson production rates are largely unaffected. We identify W h associated production followed by Higgs boson decays to photons or to leptons via W W* as potential experimental probes of these theories.

We perform a Monte Carlo simulation calculation of the critical coupling constant for the continuum ${\lambda \over 4} \phi^4_2$ theory. The critical coupling constant we obtain is $[{\lambda \over \mu^2}]_{crit}=10.24(3)$.

We study a simplified version of the Standard Electroweak Model and introduce the concept of the physical gauge invariant effective potential in terms of matrix elements of the Hamiltonian in physical states. This procedure allows an unambiguous identification of the symmetry breaking order parameter and the resulting effective potential as the energy in a constrained state. We explicitly compute the physical effective potential at one loop order and improve it using the RG. This construction allows us to extract a reliable, gauge invariant bound on the Higgs mass by unambiguously obtaining the scale at which new physics should emerge to preclude vacuum instability. Comparison is made with popular gauge fixing procedures and an ``error'' estimate is provided between the Landau gauge fixed and the gauge invariant results.

The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite gauge invariant order parameter in physical gauges. This effective potential is computed through one loop order in a model with scalars and fermions coupled to an abelian gauge theory, which serves as a simple model of the situation in electroweak theory, where vacuum stability arguments based on the scalar effective potential have been used to place lower bounds on the Higgs mass.

We examine the gauge dependence of lower bounds on the Higgs mass obtained from the requirement that the electroweak vacuum be the global minimum of the effective potential. We study a simple model, the spontaneously-broken Abelian Higgs model coupled to a chiral quark doublet in a two-parameter gauge and demonstrate that the lower Higgs mass bounds obtained in this model are dependent on the choice of gauge parameters. We discuss the significance of this result for calculations in the Standard Model.

We present a QCD-based calculation of the exclusive semileptonic decay Lambda_b -> p l nu-bar. Using the ideas of Heavy Quark Effective Theory, we discuss the factorization of the amplitude. Further, resummed Sudakov effects are put in to ensure a consistent perturbative expansion.

We study the two-impurity Kondo problem in a basis in which the electrons are written in terms of their parity w.r.t. the midpoint of the impurities. We expand the equations of motion to leading log order and show that the Kondo temperature is reduced by an increasing RKKY interaction, and for one of the electron parity channels crosses the RKKY singlet.

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