Quantum Bubble Dynamics in 2+1 Dimensional Gravity I: Geometrodynamic Approach

TL;DR

This paper performs Dirac quantization of a 2+1 dimensional bubble with a string boundary, solving ADM constraints and analyzing quantum uncertainties in the bubble's radius, highlighting significant quantum effects at the Planck scale.

Contribution

It introduces a geometrodynamic approach to quantize a bubble in 2+1 gravity, solving constraints and deriving the wave functional with quantum radius uncertainty.

Findings

Quantum uncertainty in bubble radius increases at the Planck scale.

The wave functional explicitly incorporates boundary conditions from the string.

The ADM constraints are successfully solved in this context.

Abstract

The Dirac quantization of a 2+1 dimensional bubble is performed. The bubble consists of a string forming a boundary between two regions of space-time with distinct geometries. The ADM constraints are solved and the coupling to the string is introduced through the boundary conditions. The wave functional is obtained and the quantum uncertainty in the radius of the ring is calculated; this uncertainty becomes large at the Planck scale.