New loop representations for 2+1 gravity

Abhay Ashtekar, R. Loll

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Since the gauge group underlying (2+1)-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately choosing the measure that features in the definition of the loop transform. Thus, 'old-fashioned' loop representations - -based on ordinary loops - -do exist. In the case when the spatial topology is that of a 2-torus, these can be constructed explicitly; all quantum states can be represented as functions of (homotopy classes of) loops and the scalar product and the action of the basic observables can be given directly in terms of loops.

Original languageEnglish (US)
Article number004
Pages (from-to)2417-2434
Number of pages18
JournalClassical and Quantum Gravity
Issue number10
StatePublished - 1994

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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