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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  hepth math.QA  Abstract:  Given a principal Gbundle over a smooth manifold M, with G a compact Lie group, and given a finitedimensional 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 complexvalued ambient isotopy invariants of framed oriented links in M. Moreover, this map is onetoone. Similar results hold for a C*algebraic analog, the ``holonomy C*algebra.’’ These results clarify the relation between diffeomorphisminvariant gauge theories and link invariants, and the framing dependence of the expectation values of products of Wilson loops.  Source:  arXiv, hepth/9301063  Services:  Forum  Review  PDF  Favorites 


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