Relativistic Particle in the Liouville Field

TL;DR

This paper investigates a relativistic particle in the Liouville field, exploring its symmetries, classical trajectories, and proposing a new quantization scheme that preserves classical symmetry.

Contribution

It introduces a novel quantization scheme for the relativistic particle in the Liouville field that maintains the classical $SL(2,R)/Z_2$ symmetry.

Findings

Classical trajectories described by dynamical integrals.

A gauge-invariant Hamiltonian reduction method is developed.

Quantum system reproduces the classical symmetry.

Abstract

A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used for the gauge-invariant Hamiltonian reduction. The new scheme is proposed for quantization of the reduced system. Obtained quantum system reproduces classical symmetry. Physical aspects of the model are discussed.