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Macquarie University  Department of Mathematics

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Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Fri, 15 July:  9:00 - 10:00

Higher Gauge Theory (I)
Baez, John (University of California, Riverside)

Gauge theory describes the parallel transport of point particles using the formalism of connections on bundles. In both string theory and loop quantum gravity, point particles are replaced by 1-dimensional extended objects: paths or loops in space.

This suggests that we seek some kind of `higher gauge theory' that describes the parallel transport as we move a path along a path of paths. To find the right mathematical formalism for this, it seems we must `categorify' concepts from differential geometry, replacing smooth manifolds by smooth categories, Lie groups by Lie 2-groups, Lie algebras by Lie 2-algebras, bundles by 2-bundles, sheaves by stacks or gerbes, and so on.

In this talk we provide an overview of work so far on this topic, with an emphasis on open problems and some tantalizing relationships between Lie 2-groups and central extensions of loop groups.

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See \url{http://math.ucr.edu/home/baez/street/} for talk transparencies and links to further reading material.

Typeset PDF of this abstract.