Quantum field theory on the noncommutative plane with Eq(2) symmetry

DOI10.1063/1.533201zbMath0977.81045arXivhep-th/9904132OpenAlexW3101689830MaRDI QIDQ2737890

P. Prešnajder, Masud Chaichian, A. P. Demichev

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/hep-th/9904132

zbMATH Keywords

invariant measurescalar quantum field theoryultraviolet divergencespartial wave decompositionfield theoretical action

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Model quantum field theories (81T10) Quantum field theory on lattices (81T25) Noncommutative geometry in quantum theory (81R60) Geometry of quantum groups (58B32)

Related Items (16)

Eigenvalue problem for radial potentials in space with SU(2) fuzziness ⋮ Hilbert space representations of cross product algebras. II. ⋮ Probing space–time noncommutativity in the top quark pair production at e⁺e^- collider ⋮ Loop diagrams in space with \(SU(2)\) fuzziness ⋮ DIRAC THEORY ON A SPACE WITH LINEAR LIE TYPE FUZZINESS ⋮ GAUGE THEORY ON A SPACE WITH LINEAR LIE TYPE FUZZINESS ⋮ Space-time noncommutative field theories and unitarity ⋮ Field theory on the \(q\)-deformed fuzzy sphere. II: Quantization ⋮ WILSON LOOP IN 2D NONCOMMUTATIVE GAUGE THEORIES ⋮ Quantum mechanics on space with \(SU(2)\) fuzziness ⋮ Field theory amplitudes in a space with \(SU(2)\) fuzziness ⋮ Aharonov-Bohm effect in noncommutative spaces ⋮ Poisson structure on a space with linear SU(2) fuzziness ⋮ GAUGE FIELD THEORY ON THE E_q(2)-COVARIANT PLANE ⋮ Central force problem in space with \(\mathrm{SU}(2)\) Poisson structure ⋮ Closedness of orbits in a space with SU(2) Poisson structure

Cites Work

• General concept of quantization
• Divergencies in a field theory on quantum space.
• The two-dimensional quantum Euclidean algebra
• The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function
• Noncommutative geometry from \(0\)-branes in a background \(B\)-field
• Quantum field theory on noncommutative space-times and the persistence of ultraviolet divergences
• Finite quantum field theory in noncommutative geometry
• Free \(q\)-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group
• The commutative limit of a matrix geometry
• Geometry of quantum group twists, multidimensional Jackson calculus and regularization

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