Abstract
From the time-independent current 𝒯̃(ȳ,k̄) in the quantum self-dual Yang–Mills (SDYM) theory, we construct new group-valued quantum fields Ũ(ȳ,k̄) and Ũ−1(ȳ,k̄) which satisfy a set of exchange algebras such that fields of 𝒯̃(ȳ,k̄)∼Ũ(ȳ,k̄)∂ȳŨ−1(ȳ,k̄) satisfy the original time-independent current algebra. For the correlation functions of the products of the Ũ(ȳ,k̄) and Ũ−1(ȳ,k̄) fields defined in the invariant state constructed through the current 𝒯̃(ȳ,k̄) we can derive the Knizhnik–Zamolodchikov (KZ) equations with an additional spatial dependence on k̄. From the Ũ(ȳ,k̄) and Ũ−1(ȳ,k̄) fields we construct the quantum-group generators, local, global and semi-local, and their algebraic relations. For the correlation functions of the products of the Ũ and Ũ−1 fields defined in the invariant state constructed through the semi-local quantum-group generators we obtain the quantum-group difference equations. We give the explicit solution to the two point function.
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