MEASURE FACTORS, TENSION, AND CORRELATIONS OF FLUID MEMBRANES

We study two geometrical factors needed for the correct construction o f statistical ensembles of surfaces. Such ensembles appear in the stud y of fluid bilayer membranes, though our results are more generally ap plicable. The naive functional measure over height fluctuations must b e corrected by these factors in order to give correct, self-consistent formulas for the free energy and correlation functions of the height. While one of these corrections - the Faddeev-Popov determinant - has been studied extensively, our derivation proceeds from very simple geo metrical ideas, which we hope removes some of its mystery. The other f actor is similar to the Liouville correction in string theory. Since o ur formulas differ from those of previous authors, we include some exp licit calculations of the effective frame tension and two-point functi on to show that our version indeed secures coordinate-invariance and c onsistency to lowest nontrivial order in a temperature expansion.