Canonical Quantization of (2+1)-Dimensional Gravity

TL;DR

This paper explores the quantum behavior of 2D universes with wormholes and particles, analyzing how interference of propagating amplitudes influences the most probable geometries, akin to optical diffraction patterns.

Contribution

It introduces a novel approach to quantum 2D universes using a sum over mapping class images, revealing interference effects on geometry probabilities.

Findings

Interference patterns determine probable geometries.

Wave functions are constructed from mapping class images.

Analogies to optical diffraction are established.

Abstract

We consider the quantum dynamics of both open and closed two- dimensional universes with ``wormholes'' and particles. The wave function is given as a sum of freely propagating amplitudes, emitted from a network of mapping class images of the initial state. Interference between these amplitudes gives non-trivial scattering effects, formally analogous to the optical diffraction by a multidimensional grating; the ``bright lines'' correspond to the most probable geometries.