S.Ansoldi^{1}

Dipartimento di Fisica Teorica dell'Università,

Strada Costiera 11, 34014-Trieste, Italy

Dipartimento di Fisica Teorica dell'Università,

Strada Costiera 11, 34014-Trieste, Italy

E.Spallucci^{3}

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

We discuss the relation between string quantization based on
the Schild path integral and the Nambu-Goto path integral.
The equivalence between the two approaches at the classical
level is extended to the quantum level by
a saddle-point evaluation of the corresponding path
integrals. A possible relationship between -Theory and
the quantum mechanics of string loops is pointed out. Then,
within the framework of ``loop quantum mechanics'', we
confront the difficult question as to what exactly gives rise
to the structure of spacetime. We argue that the large scale
properties of the string condensate are responsible for the
effective Riemannian geometry of classical spacetime. 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.

- 1 Introduction
- 2 Gravity/String Quantization Schemes
- 3 Eguchi's Areal Quantization Scheme

- 4 Plücker coordinates and -theory
- 5 Loop Quantum Mechanics
- 5.1 Correspondence Principle, Uncertainty Principle and the Fractalization of Quantum Spacetime
- 5.2 Superconductivity and Quantum Spacetime

- Bibliography