Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime   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.

26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci