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Functional Integral Representation Of Rough Surfaces

A functional integral representation of the statistics of rough surfaces is developed. The assumption of locality, defined in the text, produces a general form for the probability functional which automatically contains the mean square height and correlation length of the surface. The correlation function to lowest order is predicted to be a K0 modified Bessel function for all rough surfaces. The power spectrum obtained from this modified Bessel function Is In good agreement with the measured power spectra of rough surfaces. Fractal behavior occurs naturally due to the anomalous scaling of the correlation functions when higher order terms are included in the calculation.