Abstract
The Toda field is a multicomponent field in two space-time dimensions, satisfying a generalisation of the Liouville equation ∂ 2 φ + exp φ = 0. We define and solve non-perturbatively a quantum Toda field theory and its classical limit. Our technique generates an infinite number of conservation laws. By restricting the fields to one dimension we also solve the quantum mechanics and the classical mechanics of the Toda lattice.
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