No description available.

The effective potential augments the classical potential with the quantum effects of virtual particles, and permits the study of spontaneous symmetry breaking. In contrast to the standard approach where the classical potential already leads to electroweak symmetry-breaking, the Coleman-Weinberg mechanism explores quantum corrections as the source of symmetry-breaking. This thesis explores extensions of the Coleman -Weinberg mechanism to the situations with more than one Higgs doublet. These multi-Higgs models have a long history , and occur most naturally in the Minimal Supersymmetric model. Mathematical foundations of the zeta function method will be developed and then applied to regularise the one-loop computation of the effective potentials in a model with two scalar fields.

The effective potential augments the classical potential with the quantum effects of virtual particles, and permits the study of spontaneous symmetry breaking. In contrast to the standard approach where the classical potential already leads to electroweak symmetry-breaking, the Coleman-Weinberg mechanism explores quantum corrections as the source of symmetry-breaking. This thesis explores extensions of the Coleman -Weinberg mechanism to the situations with more than one Higgs doublet. These multi-Higgs models have a long history , and occur most naturally in the Minimal Supersymmetric model. Mathematical foundations of the zeta function method will be developed and then applied to regularise the one-loop computation of the effective potentials in a model with two scalar fields.

No description available.

This thesis describes a technical advance in the treatment of massive fermion two-loop calculations in QED and QCD, which allows us to reduce complicated on-shell Feynman integrals tö-a-large number-of simpië integrals, and one particularly complicated, but evaluable, one. The method extends the work of Chetyrkin and Tkachov to massive integrals, and is applicable to on-shell mass and wavefunction renormalisation. After an extensive review of the relevant areas of renormalisation, and of the rôle of quark masses in current algebra, we go on to use the extended technique to extract the fermion mass and wavefunction renormalisation constants to O(?²_s), and to relate the running and pole masses to the bare mass and to each other. We find that the ratio of the running to the pole mass may be rather smaller than might be expected, which allows us to claim a perturbative source for a larger proportion of the strange quark constituent mass than has been usual before. In passing, we extract a number of two-loop renormalisation group coefficients, and find ourselves to be in agreement with other calculations. We also find that the on-shell fermion wavefunction renormalisation constant is quite unexpectedly gauge invariant to two loops, and that it is relatively simply related to the mass renormalisation constant. We suggest that this is the result of such intricate calculations that there must be a field-theoretic explanation waiting to be uncovered. We relate our results to the effective theory of a static quark.

Since the advent of Quantum Field Theory (QFT) in the late 1940's, perturbation theory has become one of the most developed and successful means of extracting phenomenologically useful information from a QFT. In the ever- increasing enthusiasm for new phenomenological predictions, the mechanics of perturbation theory itself have often taken a back seat. It is in this light that this thesis aims to investigate some of the more fundamental properties of perturbation theory. The benefits of resumming perturbative series are highlighted by the explicit calculation of the three-jet rate in e+e- annihilation, resummed to all orders in leading and next-to-leading large logarithms. It is found that the result can be expressed simply in terms of exponentials and error functions. In general it is found that perturbative expansions in QED and QCD diverge at large orders. The nature of these divergences has been explored and found to come from two sources. The first are instanton singularities, which correspond to the combinatoric factors involved in counting Feynman diagrams at large orders. The second are renormalon singularities, which are closely linked to non-perturbative effects through the operator product expansion (OPE).By using Borel transform techniques, the singularity structure in the Borel plane for the QCD vacuum polarization is studied in detail. The renormalon singularity structure is as expected from OPE considerations. These results and existing exact large-A^/ results for the QCD Adler D-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of the QCD perturbative coefficients which is leading in b, the first coefficient of the QCD beta-function. This part is expected asymptotically to dominate the coefficients in a large-Nj expansion. Resummed results are also obtained for the e+e- R-ratio and the r-lepton decay ratio. The renormalization scheme dependence of these resummed results is discussed in some detail.

No description available.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thèse--Genève. / Bibliographical footnotes.

Thesis (Ph.D.)--Brown University, 2005. / Vita. Thesis advisor: S. G. Guralnik. Includes bibliographical references (leaves 117-118). Also available online.