This article is cited in 3 papers

Phase space of a gravitating particle and dimensional reduction at the Planck scale

A. N. Starodubtsev

St. Petersburg State University, St. Petersburg, Russia

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.

Keywords: quantum gravity, Wilson loop, magnetic monopole, curved momentum space.

DOI: 10.4213/tmf8928

 English version: Theoretical and Mathematical Physics, 2015, 185:1, 1527–1532

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