PARALLEL TRANSPORT OVER PATH SPACES

DOI10.1142/S0129055X10004156zbMath1208.81107arXiv0906.1864OpenAlexW3099639810MaRDI QIDQ3064118

Saikat Chatterjee, Amitabha Lahiri, Ambar N. Sengupta

Publication date: 20 December 2010

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

Full work available at URL: https://arxiv.org/abs/0906.1864

zbMATH Keywords

gauge theoryconnectionsparallel transportdouble categoriessurface holonomypath spaces

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of global analysis to the sciences (58Z05) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Differential graded algebras and applications (associative algebraic aspects) (16E45)

Related Items (14)

GEOMETRIC STRUCTURES ON PATH SPACES ⋮ On the global 2-holonomy for a 2-connection on a 2-bundle ⋮ Non-abelian higher gauge theory and categorical bundle ⋮ Path space connections and categorical geometry ⋮ Wilson Surfaces for Surface Knots: A Field Theoretic Route to Higher Knots ⋮ Twisted-product categorical bundles ⋮ A morphism double category and monoidal structure ⋮ Unnamed Item ⋮ Connections on decorated path space bundles ⋮ Geodesics on path spaces and double category ⋮ On higher holonomy invariants in higher gauge theory I ⋮ ON 2-HOLONOMY ⋮ Geometric prequantization on the path space of a prequantized manifold ⋮ Double Category Related to Path Space Parallel Transport and Representations of Lie 2 Groups

Cites Work

• Higher gauge theory and a non-abelian generalization of 2-form electrodynamics.
• Loop and path spaces and four-dimensional \(BF\) theories: connections, holonomies and observables
• Iterated integrals of differential forms and loop space homology
• SURFACE HOLONOMY AND GAUGE 2-GROUP
• Higher gauge theory—differential versus integral formulation
• Bundle Gerbes
• Catégories structurées

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