Topology of solutions of the Liouville equation

TL;DR

This paper explores the geometric structure of solutions to the Liouville equation, providing insights into its solution topology and implications for nonlinear field theories.

Contribution

It offers a novel analysis of the solution topology of the Liouville equation and discusses potential generalizations of geometric quantization to nonlinear field theories.

Findings

Analysis of the solution space topology for the Liouville equation

Proposals for extending geometric quantization to nonlinear fields

Results relevant to the structure of Liouville field theory

Abstract

Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.