Scalar quantum field theory on fractals

► The Wiener measure in one variable is extended to a scale invariant measure in many variables. ► Variables on the vertices of geometric shapes can take random or discrete values. ► New vertices are introduced by subdividing these figures, giving a fractal structure. ► We use fixed points associated with these measures to compute correlation functions. ► The correlations increase as an irrational power (positive/negative) of the distance.