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Local conserved densities and zero-curvature conditions for Toda lattice field theories

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
257
Identifiers
DOI: 10.1016/0550-3213(85)90347-5
Disciplines
  • Mathematics

Abstract

Abstract There is a set of two-dimensional, Lorentz-invariant Toda lattice field equations for each affine Kac-Moody algebra possessing zero-curvature gauge potentials A μ taking values in the corresponding loop algebra. A systematic procedure is presented for establishing an infinite series of local conserved densities together with the zero-curvature potential obtaining when any of these densities are alternatively used as hamiltonian density. All the corresponding hamiltonians have vanishing mutual Poisson brackets. The input needed is just the space component A x of the original A μ . The key step is the construction of a gauge transformation in the Kac-Moody loop group which makes the A μ abelian. The results are derived in a fairly general way, being independent of the group concerned or the representation of that group.

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