Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation

TL;DR

This paper discusses the complexities of solving the Wheeler-DeWitt equation in (2+1)-dimensional quantum gravity and presents evidence that it differs fundamentally from reduced phase space quantization.

Contribution

It provides insights into the solutions and interpretation of the Wheeler-DeWitt equation, highlighting its non-equivalence to reduced phase space quantization in (2+1) dimensions.

Findings

Wheeler-DeWitt equation is highly complex to solve explicitly.

Strong evidence shows non-equivalence to reduced phase space quantization.

Provides interpretative insights into quantum gravity solutions.

Abstract

In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation. In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.