Fluctuating metrics in one-dimensional manifolds

In this work we address the statistical mechanics of fluctuating metrics in two, simple, one-dimensional, manifolds: the unit interval and the unit circle. Faddeev-Popov and zeta-function regularization are used to compute explicitly the partition function without the need of any extra fields in the case of the interval. The addition of bosonic fields to the fluctuating metric background is necessary in order to accomplish complete regularization in the case of the circle. (C) 1997 American Institute of Physics.