Solution of Self-Duality Equation in Quantum-Group Gauge Theory and Quantum Harmonics
B. M. Zupnik
Abstract
We discuss the gauge theory for quantum group SUq (2)× U(1) on the quantum Euclidean space. This theory contains three physical gauge fields and one\; U(1)-gauge field with a zero field strength. We construct the quantum-group self-duality equation (QGSDE) in terms of differential forms and with the help of the field-strength decomposition. A deformed analog of the BPST-instanton solution is obtained. We consider a harmonic (twistor) interpretation of QGSDE in terms of SUq (2)/U(1) quantum harmonics. The quantum harmonic gauge equations are formulated in the framework of a left-covariant 3D differential calculus on the quantum group SUq (2).
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