Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates

Abstract

We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We investigate the effect of quantization on this curved momentum space. The coordinates are represented by non commuting, Hermitian operators on this hyperboloid. We also find that there is a smallest distance between the two particles of one half times the Planck length.

18 pages Latex, 2 eps figures

References in corpus (4)

• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
• $2+1$ Covariant Lattice Theory and t'Hooft's Formulation
• Physical Meaning of Quantum Space-Time Symmetries

Cited by in corpus (11)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
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• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• ADM approach to 2+1 dimensional gravity coupled to particles
• Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
• Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
• (2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame
• ADM approach to 2+1 dimensional gravity
• A note on broken dilatation symmetry in planar noncommutative theory
• UV dimensional reduction to two from group valued momenta
• From Lorentzian to Galilean (2+1) gravity: Drinfel'd doubles, quantisation and noncommutative spacetimes