Light-Cone Quantization of the Liouville Model

TL;DR

This paper develops a light-cone quantization approach for the Liouville model, utilizing free field representations and adapting existing methods to construct quantum operators within a restricted field momentum sector.

Contribution

It introduces a novel light-cone quantization scheme for the Liouville model, explicitly constructing quantum operators and identifying a specific restricted sector in the theory.

Findings

Quantum operators are consistently constructed in terms of free fields.

The theory's space is restricted to a specific momentum sector.

The approach adapts existing methods to the light-cone framework.

Abstract

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backl\"{u}nd transformation and adapt the approch by Braaten, Curtright and Thorn. Quantum operators of the Liouville field $\partial_{+}\phi$, $\partial_{-}\phi$, $e^{g\phi}$, $e^{2g\phi}$ are constructed consistently in terms of the free field. The Liouville model field theory space is found to be restricted to the sector with field momentum $P_{+}=-P_{-}$, $P_{+}> 0$ , which is a closed subspace for the Liouville theory operator algebra.