RADIATIVE CORRECTIONS IN HIGHER-DIMENSIONAL PHYSICS: TOPICS IN STRING THEORY AND KALUZA-KLEIN THEORY

An outstanding unsolved problem of fundamental physics is the formulation of a quantum-mechanical theory of gravitation and the incorporation of this into a unified theory of all elementary particles and their interactions. String theory and Kaluza-Klein theory are attempts to fulfill this program. In this dissertation the partition function for closed bosonic strings propagating on a flat background geometry in the critical dimension is evaluated directly as a perturbation expansion in accessible topological configurations. This work develops the general method necessary for the direct evaluation of probability amplitudes for the scattering of strings. The mathematics of surfaces required for these computations has not been widely used in elementary particle physics prior to the recent advent of interest in fundamental string theories and thus is presented in a pedagogical manner. In addition a stability analysis of self-consistent Candelas-Weinberg-type Kaluza-Klein models incorporating a spacetime-dependent background geometry is performed. It is found that quantum-mechanical corrections to the effective action may change the overall sign of the kinetic energy term. In this case the solutions of the equations of motion are unstable against perturbations in the radius of the internal space. This result motivates the investigation of the stability of Kaluza-Klein models involving arbitrary numbers of scalar and spinor fields. To one-loop order it is found that the internal space is stable only if the ratio of the number of scalar fields to the number of spinor fields lies within a certain bound which is computed for several values of the dimension of the internal space.