The 2+1 Kepler Problem and Its Quantization

Abstract

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.

59 pages, LaTeX2e, 9 eps figures

Cited by in corpus (8)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• 2+1 gravity and Doubly Special Relativity
• The Phase Space Structure of Multi Particle Models in 2+1 Gravity
• Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity
• Combinatorial quantisation of the Euclidean torus universe
• Massive particles coupled with 2+1 dimensional gravity and noncommutative field theory
• Doubly Special Relativity and quantum gravity phenomenology
• Non-commutative waves for gravitational anyons