Loop quantum mechanics and the fractal structure of quantum spacetime

We discuss the relation between string quantization based on the Schild pat h integral and the Nambu-Goto path integral. The equivalence between the tw o approaches at the classical level is extended to the quantum level by a s addle-point evaluation of the corresponding path integrals. A possible rela tionship between M-Theory and the quantum mechanics of string loops is poin ted out. Then, within the framework of "loop quantum mechanics", we confron t the difficult question as to what exactly gives rise to the structure of spacetime. We argue that the large scale properties of the string condensat e are responsible for the effective Riemannian geometry of classical spacet ime. On the other hand, near the Planck scale the condensate "evaporates", and what is left behind is a "vacuum" characterized by an effective fractal geometry. (C) 1999 Elsevier Science Ltd. All rights reserved.