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Proof of a conjecture by Lewandowski and Thiemann

Apr, 2003
22 pages
Published in:
  • Commun.Math.Phys. 249 (2004) 331-352
e-Print:
DOI:
Report number:
  • MIS-32-2003,
  • CGPG-03-3-7
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Abstract:
It is proven that for compact, connected and semisimple structure groups every degenerate labelled web is strongly degenerate. This conjecture by Lewandowski and Thiemann implies that diffeomorphism invariant operators in the category of piecewise smooth immersive paths preserve the decomposition of the space of integrable functions w.r.t. the degeneracy and symmetry of the underlying labelled webs. This property is necessary for lifting these operators to well-defined operators on the space of diffeomorphism invariant states.
Note:
  • 22 pages, 1 figure, LaTeX Report-no: MIS 32-2003, CGPG-03/3-7 Subj-class: Mathematical Physics MSC-class: 47A15 (Primary) 47A05, 81T13, 58D20, 83C45 (Secondary) Journal-ref: Commun. Math. Phys. 249 (2004) 331--352