This book examines the differential geometry of manifolds, loop
spaces, line bundles and groupoids, and the relations of this
geometry to mathematical physics. Applications presented in the
book involve anomaly line bundles on loop spaces and anomaly
functionals, central extensions of loop groups, K hler geometry of
the space of knots, and Cheeger--Chern--Simons secondary
characteristics classes. It also covers the Dirac monopole and
Dirac 's quantization of the electrical charge.
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