Dynamical quantum effects in Kaluza-Klein theories

Abstract

A general method is presented for calculating the effective action of a quantum field propagating in a time-dependent Kaluza-Klein background geometry. This method is valid when both the curvature of four-dimensional space and the logarithmic rate of change of the size of the “internal” space are much less than the curvature of the internal space. The effective action is calculated explicitly to one-loop order for a spinless Bose field in a Kaluza-Klein model for which the internal space is chosen to be the N-dimensional sphere S N for odd values of N. It is found that the quantum effects can be crucial in determining the sign of the kinetic term for the radius of the sphere.