Quantum effects in Kaluza-Klein theories

Kaluza-Klein theories are a geometrical way of combining gravitational and gauge theories. However, to be successful descriptions of nature, these theories must be quantised and the results open to sensible interpretation. This thesis is concerned with a variety of quantum effects that such a procedure engenders. The five dimensional model, considered as a proptotype of a more complete theory, exhibits several interesting effects. One loop calculations of the tower contribution to scalar expectation values demonstrates that the vacuum and self-energy, which vanished at the classical level, each receive a finite correction. However, the scalar-scalar scattering amplitude remains infinite. The latter is indicative of the inherent divergences always present in quantum gravities based on the Einstein-Hilbert Lagrangian. Gravitational and electromagnetic, Aharanov-Bohm, interference effects are unified, together with a scalar contribution to the change in the phase of the wavefunction. After the introduction of fermionic matter, chiral and conformal anomalies are calculated. The non-minimal, or Pauli coupling entails novel redefinitions of the action, the chiral anomaly also requiring currents to be altered. The conformal anomaly reinforces the non-renormalizability observed earlier. It is, however, possible to obviate these anomalies by performing a formal summation over the infinite number of virtual fermions. Finally, after reviewing the inclusion of non-abelian gauge fields, a more realistic, six dimensional model is examined. It is shown to be anomalous in its original form and in dimensionally reduced form. Dimensional reduction of the relevant topological terms is carried out and the result compared with the four dimensional chiral anomaly. The connection between the four and six dimensional anomalies is obscure.