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

摘要

We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere SU(sub q)(2)/U(1). The SU(sub q)(2)-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group SU(sub q)(2) x U(1) on the deformed Euclidean space E(sub q)(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 pre potential. 24 refs. (Atomindex citation 26:053625)