FLUCTUATING METRICS IN ONE-DIMENSIONAL MANIFOLDS

In this work we address the statistical mechanics of fluctuating metri cs in two, simple, one-dimensional, manifolds: the unit interval and t he unit circle. Faddeev-Popov and zeta-function regularization are use d to compute explicitly the partition function without the need of any extra fields in the case of the interval. The addition of bosonic fie lds to the fluctuating metric background is necessary in order to acco mplish complete regularization in the case of the circle. (C) 1997 Ame rican Institute of Physics.