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Chern–Simons theory, Vassiliev invariants, loop quantum gravity and functional integration without integration

Louis H. Kauffman

Louis H. Kauffman

Mathematics Department, University of Illinois at Chicago, Chicago, IL 60607-7045, USA

E-mail Address: kauffman@uic.edu

www.math.uic.edu/~kauffman

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https://doi.org/10.1142/S0217751X15300677Cited by:5 (Source: Crossref)

Abstract

This paper is an exposition of the relationship between Witten’s Chern–Simons functional integral and the theory of Vassiliev invariants of knots and links in three-dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory. This approach makes it possible to discuss the mathematics intrinsic to the functional integral rigorously and without functional integration. Applications to loop quantum gravity are discussed.

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