Quantum theory of geometry: III. Non-commutativity of Riemannian structures

Abhay Ashtekar, Alejandro Corichi, José A. Zapata

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110 Scopus citations


The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures - such as triad and area operators - exhibit a non-commutativity. At first sight, this feature is surprising because it implies that the framework does not admit a triad representation. To better understand this property and to reconcile it with intuition, we analyse its origin in detail. In particular, a careful study of the underlying phase space is made and the feature is traced back to the classical theory; there is no anomaly associated with quantization. We also indicate why the uncertainties associated with this non-commutativity become negligible in the semiclassical regime.

Original languageEnglish (US)
Pages (from-to)2955-2972
Number of pages18
JournalClassical and Quantum Gravity
Issue number10
StatePublished - Oct 1998

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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