Geodesic
Phase space of a~gravitating particle and dimensional reduction at the~Planck scale
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 192-198

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Several approaches to quantizing general relativity suggest that quantum gravity at very short distances behaves effectively as a two-dimensional theory. The mechanism of this dimensional reduction is not yet understood. We attempt to explain it by studying the phase space of a test particle coupled to a gravitational field. The general relativity constraints relate the particle energy–momentum to some curvature invariants taking values in a group manifold. Some directions in the resulting momentum space turn out to be compact, which leads to a kind of "inverse Kaluza–Klein reduction" at short distances.
Keywords: quantum gravity, Wilson loop, magnetic monopole, curved momentum space. 
@article{TMF_2015_185_1_a17,
     author = {A. N. Starodubtsev},
     title = {Phase space of a~gravitating particle and dimensional reduction at {the~Planck} scale},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {192--198},
     publisher = {mathdoc},
     volume = {185},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a17/}
}
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A. N. Starodubtsev. Phase space of a~gravitating particle and dimensional reduction at the~Planck scale. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 192-198. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a17/