Two-particle quantum mechanics in gravity using non-commuting coordinates

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

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. ...

One-particle Hilbertspace of 2+1 dimensional gravity using non-commuting coordinates

In 1963 Staruszkiewicz [1] considered general relativity in 2+1 dimensions for the first time. He solved the gravitational field surrounding a point-particle and found that is represents a conical spacetime. The subject was revived in 1984 by Deser, Jackiw and ’t Hooft [2] where it was shown that multiparticle solutions can be constructed by cutting wedges out of spacetime and identifying the b...

Two-particle interference in standard and Bohmian quantum mechanics

The compatibility of standard and Bohmian quantum mechanics has recently been challenged in the context of two-particle interference, both from a theoretical and an experimental point of view. We analyze different setups proposed and derive corresponding exact forms for Bohmian equations of motion. The equations are then solved numerically, and shown to reproduce standard quantum-mechanical res...

Non-Perturbative Two-Dimensional Quantum Gravity, Again

Gerbes, Quantum Mechanics and Gravity

We prove that invariance of a quantum theory under the semiclassical vs. strong– quantum duality S/~ ←→ ~/S, where S is the classical action, is equivalent to noncommutativity (of the Heisenberg–algebra type) of the coordinates of the space on which S is defined. We place these facts in correspondence with gerbes and Neveu– Schwarz B–fields and discuss their implications for a quantum theory of...