Gauged Laplacians on quantum Hopf bundles

DOI10.1007/s00220-008-0672-5zbMath1180.58004arXiv0801.3376OpenAlexW2090061134MaRDI QIDQ842447

Alessandro Zampini, Giovanni Landi, Cesare Reina

Publication date: 25 September 2009

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3376

zbMATH Keywords

quantum sphereCasimir operatorgauged Laplacianmonopole connectionquantum Hopf bundle

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Noncommutative geometry methods in quantum field theory (81T75) Noncommutative geometry in quantum theory (81R60) Geometry of quantum groups (58B32) Ring-theoretic aspects of quantum groups (16T20)

Related Items

EXAMPLES OF HODGE LAPLACIANS ON QUANTUM SPHERES ⋮ Yang-Mills-scalar-matter fields in the quantum Hopf fibration ⋮ Dimensional reduction over the quantum sphere and non-Abelian \(q\)-vortices ⋮ Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces ⋮ Quantum bundle description of quantum projective spaces ⋮ Anti-selfdual connections on the quantum projective plane: monopoles ⋮ Twisted sigma-model solitons on the quantum projective line ⋮ CALCULI, HODGE OPERATORS AND LAPLACIANS ON A QUANTUM HOPF FIBRATION ⋮ Examples of gauged Laplacians on noncommutative spaces ⋮ HODGE DUALITY OPERATORS ON LEFT-COVARIANT EXTERIOR ALGEBRAS OVER TWO- AND THREE-DIMENSIONAL QUANTUM SPHERES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Principal homogeneous spaces for arbitrary Hopf algebras
• Differential calculus on quantum spheres
• On the noncommutative spin geometry of the standard Podleś sphere and index computations
• Quantum spheres
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials
• Noncommutative differential geometry on the quantum two sphere of Podlès. I: An algebraic viewpoint
• Quantum differentials and the \(q\)-monopole revisited
• Quantum group gauge theory on quantum spaces
• Noncommutative Riemannian and spin geometry of the standard \(q\)-sphere
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Bundles over quantum sphere and noncommutative index theorem
• Projective module description of the \(q\)-monopole
• Spin-Hall effect with quantum group symmetries
• A local index formula for the quantum sphere
• Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere