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• W1995621679 abstract "Affine Toda theories with imaginary couplings associate with any simple Lie Algebra g generalisations of sine-Gordon theory which are likewise integrable and posses soliton solutions. The solitons are “created” by exponentials of quantities F̂i(z) which lie in the untwisted affine Kac-Moody algebra ĝ and ad-diagonalise the principal Heisenberg subalgebra. When g is simply laced and highest-weight irreducible representations at level one are considered, F̂i(z) can be expressed as a vertex operator whose square vanishes. This nilpotency property is extended to all highest-weight representations of all affine untwisted Kac-Moody algebras in the sense that the highest non-vanishing power becomes proportional to the level. As a consequence, the exponential series mentioned terminates and the soliton solutions have a relatively simple algebraic expression whose properties can be studied in a general way. This means that various physical properties of the soliton solutions can be directly related to the algebraic structure. For example, a classical version of Dorey's fusing rule follows from the operator product expansion of two F̂'s, at least when g is simply laced. This adds to the list of resemblances of the solitons with respect to the particles which are the quantum excitations of the fields." @default.
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• W1995621679 date "1993-12-01" @default.
• W1995621679 modified "2023-09-27" @default.
• W1995621679 title "Affine Toda solitons and vertex operators" @default.
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• W1995621679 doi "https://doi.org/10.1016/0550-3213(93)90541-v" @default.
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