A New Class of Two-Dimensional Noncommutative Spaces

Abstract

We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent states we are able to take the continuum limit, where we recover the punctured plane with non constant Poisson structures.

19 pages

References in corpus (6)

• Noncommutative Field Theory
• Quantum Hall states as matrix Chern-Simons theory
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Absence of the Holographic Principle in Noncommutative Chern-Simons Theory
• Scalar Multi-Solitons on the Fuzzy Sphere
• Poisson Chern-Simons Gauge Theory

Cited by in corpus (11)

• The Fuzzy Disc
• Exact operator bosonization of finite number of fermions in one space dimension
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Edge Currents in Non-commutative Chern-Simons Theory from a New Matrix Model
• Noncommutative $Ad{S}^3$ with Quantized Cosmological Constant
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Extended Voros product in the coherent states framework
• A Perturbative Approach to Fuzzifying Field Theories
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Covariance of noncommutative Grassmann star product