Locally Noncommutative Space-Times

Abstract

Localized noncommutative structures for manifolds with connection are constructed based on the use of vertical star products. The model's main feature is that two points that are far away from each other will not be subject to a deviation from classical geometry while space-time becomes noncommutative for pairs of points that are close to one another.

28 pages, 7 figures

References in corpus (9)

• Deformation quantization of Poisson manifolds, I
• The quantum structure of spacetime at the Planck scale and quantum fields
• Construction of non-Abelian gauge theories on noncommutative spaces
• Noncommutative gauge theory for Poisson manifolds
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• States and representations in deformation quantization
• Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
• Hermitian star products are completely positive deformations
• Morita Equivalence, Picard Groupoids and Noncommutative Field Theories

Cited by in corpus (5)

• Coherent representation of fields and deformation quantization
• Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• A Deformation Quantization for Non-Flat Spacetimes and Applications to QFT
• On Finite Noncommutativity in Quantum Field Theory