Summary: We have constructed a quantum field theory for the self-dual Yang-Mills system in terms of the group-valued fields \(\hat J\). They satisfy exchange algebras, of which the structure matrices \(\hat R\) satisfy Yang-Baxter equations. We show that the fields \(\hat J\) form noncommutative vector spaces of a local quantum group and their products at short distances have nontrivial critical exponents. We obtain the quantum Hamiltonian and equations of motion; identify the generators for their symmetries; and construct the affine Lie algebra currents, Virasoro algebra fields, and hierarchies of linear and nonlinear systems.