MSc defense by David Ribers

On Lattice String Theory and Quantum Fields on a World-Line

This thesis explores the theory of the relativistic particle from the view-point of a one-dimensional quantum field theory (QFT) living on the particle world-line. By expanding the geometric action through the introduction of a world-line metric and a Lagrange multiplier we find a rich and formally non-renormalizable QFT in need of gauge-fixing due to the reparametrization invariance of the original action. We consider the large D limit in which the non-renormalizabiliy can be circumvented. By splitting the maps from the world-line parameter space to target-space into classical (background) and quantum components we attempt reproduce the results of J. Ambjørn and Y. Makeenko ["Scaling behavior of regularized bosonic strings",  Phys. Rev. D, 93:066007] to first order in perturbation theory by comptuing one-loop corrections to the propagator of the background field. We find the theory to exhibit an expected freedom in terms of the joint renormalization of the mass parameter and the background field strength, though a natural renormalization of both arises when considering the theory as one-dimensional gravity coupled to D scalar fields.