Light-cone quantisation of the Liouville and Toda field theories

Abstract

The Toda field is a multicomponent field in two space-time dimensions satisfying a generalisation of the Liouville equation ϖ 2 ϕ + exp ϕ = 0. We define the quantum field theory, and solve for the fields in terms of their initial values on a forward light-cone, demonstrating that our solution is regular. We give an explicit result for the Liouville equation which is the quantum version of the well-known classical solution. We also discuss the energy-momentum spectrum, and the conformal properties of the theory.