

Preprint 32/2003
Proof of a Conjecture by Lewandowski and Thiemann
Christian Fleischhack
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Submission date: 31. Mar. 2003
Pages: 24
published in: Communications in mathematical physics, 249 (2004) 2, p. 331-352
DOI number (of the published article): 10.1007/s00220-004-1052-4
Bibtex
MSC-Numbers: 47A15, 47A05, 81T13, 58D20, 83C45
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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.arXiv number: math-ph/0304002