Path space connections and categorical geometry. (English) Zbl 1280.81087
Summary: We develop a new differential geometric structure using category theoretic tools that provides a powerful framework for studying bundles over path spaces. We study a type of connection forms, given by Chen integrals, over path spaces by placing such forms within a category-theoretic framework of principal bundles and connections. A new notion of ’decorated’ principal bundles is introduced, along with parallel transport for such bundles, and specific examples in the context of path spaces are developed.
MSC:
| 81S40 | Path integrals in quantum mechanics |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 46M20 | Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 55R91 | Equivariant fiber spaces and bundles in algebraic topology |
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