Hamiltonian Analysis of SL(2,R) Symmetry in Liouville Theory

TL;DR

This paper performs a Hamiltonian analysis of Liouville theory, constructing SL(2,R) symmetry generators in different gauge choices, clarifying differences between Hamiltonian approaches based on various time parameters.

Contribution

It introduces a Hamiltonian framework for Liouville theory that explicitly constructs SL(2,R) symmetry generators in different gauge fixings, highlighting differences in Hamiltonian approaches.

Findings

Constructed SL(2,R) symmetry generators in light-cone and other gauges.

Clarified differences between Hamiltonian approaches with different time choices.

Provided a systematic method for symmetry analysis in Liouville theory.

Abstract

We consider a Hamiltonian analysis of the Liouville theory and construction of symmetry generators using Castellani's method. We then discuss the light-cone gauge fixed theory. In particular, we clarify the difference between Hamiltonian approaches based on different choices of time, $\xi^0$ and $\xi^+$. Our main result is the construction of SL(2,R) symmetry generators in both cases. ( Lectures presented at the Danube Workshop '93, June 1993, Belgrade, Yugoslavia.)