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

1994/12/22 by Б. М. Зупник, B. M. Zupnik, Zupnik, B. M.
Mathematics · Physics and Astronomy · #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #advanced mathematical theories #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9412010

1+10 pages, LATEX

arxiv created 1994/12/22 · openalex publication_date 1994/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere SU_q (2)/U(1) . The SU_q (2)-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group SU_q (2)× U(1) on the deformed Euclidean space E_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 prepotential.

Related

• Differential Calculus on Quantum Spheres
• Covariant first order differential calculus on quantum Euclidean spheres
• Differential Calculi on the Quantum Group SU_q(2) and Global U(1)-covariance
• Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and Minimal Gauge Theory
• Quantum Deformations of the Self-Duality Equation and Conformal Twistors