No description available.

This thesis is a study of the validity and application of the on-shell recursion relations within the theory of General Relativity. These relations are also known as the Britto-Cachazo-Feng-Witten (BCFW) relations. They reduce the calculation of a tree-level graviton scattering amplitude into the evaluation of two smaller physical amplitudes and of a propagator. With multiple applications of the recursion relations, amplitudes can be uniquely constructed from fundamental three-graviton amplitudes. The BCFW prescriptions were first applied to gauge theory. We thus provide a self-contained description of their usage in this context. We then generalize the proof of their validity to include gravity. The BCFW recursion relations can then be used to reconstruct the full theory from cubic vertices. We finally describe how these three-graviton vertices can be determined uniquely from Poincare symmetries.

This thesis is a study of the validity and application of the on-shell recursion relations within the theory of General Relativity. These relations are also known as the Britto-Cachazo-Feng-Witten (BCFW) relations. They reduce the calculation of a tree-level graviton scattering amplitude into the evaluation of two smaller physical amplitudes and of a propagator. With multiple applications of the recursion relations, amplitudes can be uniquely constructed from fundamental three-graviton amplitudes. The BCFW prescriptions were first applied to gauge theory. We thus provide a self-contained description of their usage in this context. We then generalize the proof of their validity to include gravity. The BCFW recursion relations can then be used to reconstruct the full theory from cubic vertices. We finally describe how these three-graviton vertices can be determined uniquely from Poincare symmetries.

Thesis (Ph.D.)--University of California, Berkeley, 1962. / "UC-34 Physics" -t.p. "TID-4500 (17th Ed.)" -t.p. Includes bibliographical references (p. 59-60).

Thesis--University of California, Berkeley, 1962. / "UC-34 Physics" -t.p. "TID-4500 (18th Ed.)" -t.p. Includes bibliographical references (p. 52).

We consider scattering in $R^n$, $nge 2$, described by the Schr"odinger operator $P(h)=-h^2Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $hto 0$ of the scattering amplitude $f(omega_-,omega_+;lambda,h)$ $omega_+neqomega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity. / Wir betrachten Streuung in $R^n$, $nge 2$, beschrieben durch den Schr"odinger operator $P(h)=-h^2Delta+V$, wo $V$ ein kurzreichweitiges Potential ist. Mit Hilfe von Maslov Theorie erhalten wir eine geometrische Formel fuer die semiklassische Asymptotik ($hto 0$) der Streuamplitude $f(omega_-,omega_+;lambda,h)$ ($omega_+neqomega_-$) welche auch bei Vorhandensein von Fokalpunkten bei Unendlich (Kaustiken) gueltig bleibt.

Includes bibliographical references (p. 10). / "Physics and Mathematics" -t.p. "TID-4500 (15th Ed.)" -t.p.

Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are related to those of N = 4 super-Yang-Mills (SYM) theory. This makes all-plus amplitudes a useful testing ground for new methods of simplifing more general classes of amplitudes. In this thesis we consider three new approaches, focusing on the structure before integration. We begin with the planar (leading-colour) sector. A D-dimensional local-integrand presentation, based on four-dimensional local integrands developed for N = 4 SYM, is developed. This allows us to compute the planar six-gluon, two-loop all-plus amplitude. Its soft structure is understood before integration, and we also perform checks on collinear limits. We then proceed to consider subleading-colour structures. A multi-peripheral colour decomposition is used to find colour factors based on underlying tree-level amplitudes via generalised unitarity cuts. This allows us to find the integrand of the full-colour, two-loop, five-gluon all-plus amplitude. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. Finally, we consider representations satisfying colour-kinematics duality. We discuss obstacles to finding such numerators in the context of the same five-gluon amplitude at two loops. The obstacles are overcome by adding loop momentum to our numerators to accommodate tension between the values of certain cuts and the symmetries of certain diagrams. Control over the size of our ansatz is maintained by identifying a highly constraining, but desirable, symmetry property of our master numerator.

The aim of this research is to develop a method for expanding the Jost functions as a Taylor-type power series on the complex angular momentum plane. From this method in conjunction with the Watson transformation, we were able to express the scattering amplitude as a sum of the background and pole terms, furthermore, this method propose a way of evaluating, numerically, the pole term. To demonstrate how this method may be applied, we considered the Born approximation. We found out that the developed method improved the Born approximation at large scattering angles. Therefore, this method is useful when the di fferential cross section of the background term fails to converge to that of the exact diff erential cross section at large scattering angles. / Dissertation (MSc)--University of Pretoria, 2016. / National Research Foundation (NRF) / Physics / MSc

The electromagnetic form factors in elastic electron-proton scattering are used to determine the finite size of the proton. Through the use of Feynman Diagrams and Fermi's "golden rule", several key results for cross sections of elastic electron scattering will be re-derived. This will ultimately lead to the calculation for the Rosenbluth formula, that describes in detail the process of electron-proton scattering. Furthermore, the process used for determining the size of the proton from the form factors will be shown. In addition, a recent paper by R. Jaffe, which argues the validity of this process, will be discussed in detail. / Physics