Contact interactions for point particles and strings

We investigate delta-function contact interactions for theories of point particles and of strings. These interactions are introduced to reformulate the conventional theory of classical electrodynamics in terms of particles and strings which interact when they intersect. Upon quantisation we find that the tensionless limit of the spinning string theory generates well-known gauge invariant quantities in the worldline formulation of quantum field theory. Despite the off-shell nature of the interaction we find that the string theory does not encounter the expected break-down of conformal invariance. We further develop worldline techniques for non-Abelian theories and consider first quantised versions of some grand unified theories. This work can be seen as initiating the construction of a first-quantised version of the quantum field theory describing the standard model.