The extended loop group: An infinite dimensional manifold associated with the loop space

DOI10.1007/BF02108073zbMath0792.58011arXivgr-qc/9303010MaRDI QIDQ1313267

Rodolfo Gambini, Cayetano Di Bartolo, Jorge Griego

Publication date: 16 August 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/9303010

zbMATH Keywords

quantum gravitygauge theoryknot invariantsloop spacesinfinite dimensional Lie groupequivalence class of closed oriented paths

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Applications of manifolds of mappings to the sciences (58D30) Manifolds of mappings (58D15)

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Cites Work

• Unnamed Item
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• Quantum electrodynamics without potentials
• Quantum field theory and the Jones polynomial
• Ashtekar formulation of general relativity and loop-space nonperturbative quantum gravity: a report
• A polynomial invariant for knots via von Neumann algebras
• A new polynomial invariant of knots and links
• On the Loop Space Formulation of Gauge Theories
• Knot invariants as nondegenerate quantum geometries