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Discreteness of area in noncommutative space

Authors
Journal
Physics Letters B
0370-2693
Publisher
Elsevier
Publication Date
Volume
676
Identifiers
DOI: 10.1016/j.physletb.2009.04.045
Keywords
  • Theory
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a “minimum-area principle”. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.

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