Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime

Details Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime

1998-03-27

arxiv.org/abs/hep-th/9803229v1

Chaos Solitons Fractals 10 (1999) 197

Physics

High Energy Physics

High Energy Physics - Theory

19pag. ReVTeX, 1fig. Invited paper to appear in the special issue of {\it Chaos, Solitons and Fractals} on ``Super strings, M,

Scientific paper

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 M-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.

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