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Link Invariants, Holonomy Algebras and Functional Integration | | John C. Baez
; | | Date: |
15 Dec 1992 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | Given a principal G-bundle over a smooth manifold M, with G a compact Lie group, and given a finite-dimensional unitary representation of G, one may define an algebra of functions on the space of connections modulo gauge transformations, the ``holonomy Banach algebra’’ H_b, by completing an algebra generated by regularized Wilson loops. Elements of the dual H_b* may be regarded as a substitute for measures on the space of connections modulo gauge transformations. There is a natural linear map from diffeomorphism- invariant elements of H_b* to the space of complex-valued ambient isotopy invariants of framed oriented links in M. Moreover, this map is one-to-one. Similar results hold for a C*-algebraic analog, the ``holonomy C*-algebra.’’ These results clarify the relation between diffeomorphism-invariant gauge theories and link invariants, and the framing dependence of the expectation values of products of Wilson loops. | | Source: | arXiv, hep-th/9301063 | | Services: | Forum | Review | PDF | Favorites | |
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