Thesis (Ph. D.)--Oregon State University, 1977. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 58).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 93-100).

Infrared (IR) singularities are a salient feature of any field theory containing massless fields. In Quantum Chromodynamics (QCD), such singularities give rise to logarithmic corrections to physical observables. For many interesting observables, these logarithmic corrections grow large in certain areas of phase space, threatening the stability of perturbative expansion and requiring resummation. It is known, however, that IR singularities are universal and exponentiate, allowing one to study their all-order behaviour in any gauge theory by means of so-called webs: specific linear combinations of Feynman diagrams with modified colour factors corresponding to those of fully connected trees of gluons. Furthermore, infrared singularities factorise from the hard cross-section into soft and jet functions. The soft function may be calculated as a correlator of Wilson lines, vastly simplifying the computation of IR poles and allowing analytic computation at high loop order. Renormalisation group equations then allow the definition of a soft anomalous dimension, which may then be directly computed either through differential equations or by a direct, diagrammatic method. Soft singularities are highly constrained by rescaling symmetry, factorisation, Bose symmetry, and high energy- and collinear limits. In the case of light-like external partons, this leads directly to a set of constraint equations for the soft anomalous dimension, the simplest solution of which is a sum over colour dipoles. At two loops, this so-called dipole formula is the only admissible solution, leading to the complete cancellation of any tripole colour structure. Corrections beyond the dipole formula may first be seen at three loops, and must take the form of weight five polylogarithmic functions of conformal invariant cross-ratios, correlating four hard jets through a quadrupole colour structure. In this thesis we calculate this first correction beyond the dipole formula by considering three-loop multiparton webs in the asymptotic limit of light-like external partons. We do this by computing all relevant webs correlating two, three and four lines at three loop order by means of an asymptotic expansion of Mellin-Barnes integrals near the limit of light-like external partons. We find a remarkably simple result, expressible entirely in terms of Brown's single-valued harmonic polylogarithms, consistent with high-energy and forward scattering limits. Finally, we study the behaviour of this correction in the limit of two partons becoming collinear, and discuss collinear factorisation properties.

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow up. In dimension 2, V. Shokurov proved that weakly exceptional quotient singularities are exactly those of types Dn, E6, E7, E8. This thesis classifies the weakly exceptional quotient singularities in dimensions 3, 4 and 5, and proves that in any prime dimension, all but finitely many irreducible groups give rise to weakly exceptional singularities. It goes on to provide an algorithm that produces such a classification in any given prime dimension.

Chan Sik Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 38-41). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Preliminary analysis --- p.11 / Chapter 3 --- Liapunov-Schmidt Reduction --- p.19 / Chapter 4 --- The reduced problem: A Minimizing Procedure --- p.32 / Chapter 5 --- Proof of the theorem 1.2 --- p.35 / Bibliography --- p.38

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 112-113. / by Barbara R. Peskin. / Ph.D.

Singularities have been a long-standing problem in general relativity. In all other fields of physics, singularities can be easily located and avoided; in general relativity, singularities have an impact on the creation of the manifold, but, by definition, are not even part of real spacetime. Moreover, all singularities in general relativity cannot be treated in the same manner; thus, the classification of singularities is essential in order to understand them. One important class of singularities is curvature singularities, which, in some cases, can be subclassified as central, shell focusing or shell crossing singularities. We propose to further classify curvature singularities as either gravitational or non-gravitational. In general relativity, a curvature singularity is ``located'' where the scalar invariants of the spacetime are undefined. The gradient field of a non-zero scalar invariant can then be calculated, and the end points of the associated integral curves can be determined. If integral curves are attracted to (i.e. intersect) the singularity, then it is a gravitational singularity; if the integral curves avoid the singularity, then it is a non-gravitational singularity. We will test our method by analysing several different spacetimes, including Friedman-Lemaitre-Robertson-Walker, Schwarzschild, self-similar Vaidya, self-similar Tolman-Bondi, non-self-similar Vaidya, and Kerr spacetimes. We find that in every case studied, the integral curves have specific end points, therefore they can be used to classify a curvature singularity as gravitational or non-gravitational. In Friedman-Lemaitre-Robertson-Walker and Schwarzschild spacetimes, we determined that the a(t) = 0 and r = 0 singularities, respectively, are gravitational singularities. In Vaidya and Tolman-Bondi spacetime, we determine that the massless shell focusing singularities are non-gravitational singularities and that the central singularities (which have mass) are gravitational singularities. We also find that the non-gravitational singularities are the only singularities that have the possibility of being naked. In summary, we can determine which singularities are gravitational and which are non-gravitational by our method of examining the end points of the integral curves, which are constructed from the gradient field of scalar invariants. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2008-07-21 17:13:27.992

Thesis--Bonn. / Vita. Includes bibliographical references (p. 91-94).

Thesis--Bonn. / Vita. Includes bibliographical references (p. 91-94).