Abstract
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.
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 1, pp. 192–198, October, 2015.
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Starodubtsev, A.N. Phase space of a gravitating particle and dimensional reduction at the Planck scale. Theor Math Phys 185, 1527–1532 (2015). https://doi.org/10.1007/s11232-015-0362-3
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DOI: https://doi.org/10.1007/s11232-015-0362-3