Proof of a Conjecture by Lewandowski and Thiemann

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.

22 pages, 1 figure, LaTeX

References in corpus (3)

• Diffeomorphism invariant Quantum Field Theories of Connections in terms of webs
• Hyphs and the Ashtekar-Lewandowski Measure
• Stratification of the Generalized Gauge Orbit Space

Cited by in corpus (4)

• Background Independent Quantum Gravity: A Status Report
• Representations of the Weyl Algebra in Quantum Geometry
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• A Fock space structure for the diffeomorphism invariant Hilbert space of loop quantum gravity and its applications