Hyphs and the Ashtekar-Lewandowski measure

DOI10.1016/S0393-0440(00)00036-XzbMath1012.58007arXivmath-ph/0001007OpenAlexW2075921405MaRDI QIDQ1867202

Christian Fleischhack

Publication date: 2 April 2003

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0001007

zbMATH Keywords

graphmeasurepathlattice gauge theoriesAshtekar connectionsgeneralized conncectionshyphnew parallel transports

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Connections (general theory) (53C05) Measures (Gaussian, cylindrical, etc.) on manifolds of maps (58D20)

Related Items (9)

Proof of a conjecture by Lewandowski and Thiemann ⋮ Loop quantization and symmetry: configuration spaces ⋮ Regular connections among generalized connections ⋮ Representations of the Weyl algebra in quantum geometry ⋮ On spectral triples in quantum gravity. II. ⋮ ON THE STRUCTURE OF THE SPACE OF GENERALIZED CONNECTIONS ⋮ Kinematical Foundations of Loop Quantum Cosmology ⋮ An infinite-dimensional calculus for generalized connections on hypercubic lattices ⋮ On the spectrum of holonomy algebras

Cites Work

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• Functional integration on spaces of connections
• A new type of loop independence and SU(N) quantum Yang–Mills theory in two dimensions
• Comment on a paper of Ashtekar and Isham
• Representations of the holonomy algebras of gravity and nonAbelian gauge theories
• Quantum theory of geometry: I. Area operators
• Diffeomorphism-invariant quantum field theories of connections in terms of webs
• Projective techniques and functional integration for gauge theories
• Stratification of the generalized gauge orbit space

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