Edge States from Defects on the Noncommutative Plane

Abstract

We illustrate how boundary states are recovered when going from a noncommutative manifold to a commutative one with a boundary. Our example is the noncommutative plane with a defect, whose commutative limit was found to be a punctured plane - so here the boundary is one point. Defects were introduced by removing states from the standard harmonic oscillator Hilbert space. For Chern-Simons theory, the defect acts as a source, which was found to be associated with a nonlinear deformation of the $w_{\infty }$ algebra. The undeformed $w_{\infty }$ algebra is recovered in the commutative limit, and here we show that its spatial support is in a tiny region near the puncture.

9 pages; Talk presented by at the conference ``Space-time and Fundamental Interactions: Quantum Aspects'' in honor of A.P. Balachandran's 65th birthday, Vietri sul Mare, Salerno, Italy 26th-31st May, 2003

References in corpus (4)

• Noncommutative Field Theory
• On Level Quantization for the Noncommutative Chern-Simons Theory
• Chern-Simons Theories on Noncommutative Plane
• W-Infinity Algebras from Noncommutative Chern-Simons Theory

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