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Differential Calculus on the Quantum Sphere and Deformed Self-Duality Equation

B. M. Zupnik

q-algarXiv:q-alg/9412010

Abstract

We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere SUq (2)/U(1) . The SUq (2)-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group SUq (2)× U(1) on the deformed Euclidean space Eq (4). A q-generalization of the harmonic-gauge-field formalism is suggested . This formalism is applied for the harmonic (twistor) interpretation of the quantum-group self-duality equation (QGSDE). We consider the zero-curvature representation and the general construction of QGSDE-solutions in terms of the analytic prepotential.

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