3pm - 4pm
Wednesday 30 May 2018
From Gauge Theory to Higher Gauge Theory
Professor Christian Saemann (Heriot-Watt University) will be speaking.
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- Prof Christian Saemann (Heriot-Watt University)
A gauge theory is a dynamical principle on a set of fields which exhibits a large redundancy governed by a Lie group of symmetries.
The prime examples of gauge theories are Maxwell's equations as well as the Standard Model of Elementary Particles. Mathematically, the set of fields is composed of a connection on a principal fibre bundle as well as sections of associated vector bundles.
Cartan gave a very useful local description of the kinematical data of gauge theory making use of differential graded algebras. This description is "good" from a category theoretical perspective as it immediately allows for vast generalisations to higher gauge theories as required, e.g., in string theory.
I will begin my talk with an elementary review of gauge theory. I will then recall the kinematical data underlying every gauge theory and show how they arise in Cartan's description. The higher generalisation is then obtained in a few simple steps. I will end with a few pointers on how the local description of higher gauge theory globalises to principal infinity-bundles.