Abstract
The first part of this thesis contains two new techniques for the calculation of scattering amplitudes in quantum field theories. These methods were inspired by the recent proposal of a correspondence between the weakly coupled regime of the maximally supersymmetric four dimensional gauge theory and a string theory in twistor space. We show how generalised unitarity cuts in D = 4 − 2² dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We then show that the ideas of the Britto, Cachazo, Feng and Witten tree-level on-shell recursion relation can also be applied to the calculation of finite one-loop amplitudes in pure Einstein gravity. The second part of this thesis is a study of the nonabelian phenomena associated with D-branes. Specifically we study the nonabelian bionic brane intersection in which a stack of many coincident D1-branes expand via a non-commutative spherical configuration into a collection of higher dimensional D-branes orthogonal to the original stack of D1-branes. We suggest a construction of monopoles in dimension 2k+1 from fuzzy funnels. We then perform two charge calculations related to this construction. This leads to a new formula for the symmetrised trace quantity. This new formula for the symmetrised trace is then used to study the collapse of a spherical bound state of D0-branes.