Field theory on the \(q\)-deformed fuzzy sphere. II: Quantization

DOI10.1016/S0393-0440(02)00023-2zbMath1130.81347arXivhep-th/0103164OpenAlexW2005843650MaRDI QIDQ697834

Harald Grosse, John Madore, Harold Steinacker

Publication date: 17 September 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0103164

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative geometry methods in quantum field theory (81T75) Noncommutative geometry in quantum theory (81R60) Geometry of quantum groups (58B32)

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Cites Work

• Solutions of Klein-Gordon and Dirac equations on quantum Minkowski spaces
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum spheres
• More on quantum groups from the quantization point of view
• On finite 4D quantum field theory in non-commutative geometry
• String theory and noncommutative geometry
• Non-commutative world-volume geometries: branes on SU(2) and fuzzy spheres
• Free particle in \(q\)-deformed configuration space
• Wave equations on \(q\)-Minkowski space
• Identical particles and quantum symmetries
• Quantum field theory on the noncommutative plane with Eq(2) symmetry
• THE SO_q(N, R)-SYMMETRIC HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE ${\bf R}_q^N$ AND ITS HILBERT SPACE STRUCTURE
• Quantum algebra deforming maps, Clebsch–Gordan coefficients, coproducts, R and U matrices
• The fuzzy sphere
• DRINFEL'D TWIST AND q-DEFORMING MAPS FOR LIE GROUP COVARIANT HEISENBERG ALGEBRAE
• Quantum anti-de Sitter space and sphere at roots of unity
• Braided quantum field theory
• Field theory on the \(q\)-deformed fuzzy sphere. I.
• Nonassociative star product deformations for D-brane world-volumes in curved backgrounds.
• Brane dynamics in background fluxes and non-commutative geometry
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