Wave Functions of the Induced 2D-Gravity

TL;DR

This paper analyzes the wave functions of induced 2D gravity using minisuperspace quantization, revealing phase transition phenomena in the probability distribution at a critical parameter value.

Contribution

It provides explicit solutions to the Wheeler-DeWitt equation in 2D gravity and explores their properties, including phase transition behavior.

Findings

Solution expressed via Bessel functions of real or imaginary order

Identification of a phase transition at the critical point =0

Analysis of probability distribution properties in the model

Abstract

We consider the induced $2$d-gravity in the minisuperspace approach. The general solution to the Wheeler-DeWitt equation is given in terms of different kind of Bessel functions of purely real or imaginary orders. We study the properties of the corresponding probability distribution finding a kind of phase transition at the critical point $\nu=0$.