Characterizing Yang-Mills fields by stochastic parallel transport

DOI10.1006/jfan.1997.3238zbMath0913.60042OpenAlexW2043742783MaRDI QIDQ1266274

Robert Otto Bauer

Publication date: 16 September 1998

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1997.3238

zbMATH Keywords

stochastic parallel transportgauge orbitYang-Mills fieldsdriving Brownian motion

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Martingales and classical analysis (60G46)

Related Items (9)

Stochastic Lévy differential operators and Yang–Mills equations ⋮ Yang-Mills fields and stochastic parallel transport in small geodesic balls. ⋮ Yang-Mills fields and random holonomy along Brownian bridges ⋮ Lévy Laplacians, holonomy group and instantons on 4-manifolds ⋮ A probabilistic approach to the Yang-Mills heat equation. ⋮ Applications of Lévy differential operators in the theory of gauge fields ⋮ Lévy Laplacians and instantons on manifolds ⋮ Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields ⋮ An analogue of Yi's theorem to holomorphic mappings

Cites Work

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• Large deviations and the Malliavin calculus
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• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Yang-Mills gauge fields as harmonic functions for the Lévy Laplacian
• Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
• Stochastic integrators with stationary independent increments

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