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Weekly seminars

Gauge Theories on Lie Algebroids

par Jeremy Attard (CPT Marseille)

Auditorium (Annecy-le-Vieux)



9 chemin de Bellevue 74940 ANNECY LE VIEUX

Gauge theories of fundamental interactions (except gravitation) are usually written in the geometric framework of principal and associated fibre bundles, and gravitation is usually written in the framework of riemannian geometry. We present a new way of writting such theories which offers great possibilities : transitive Lie algebroids. In this geometrico-algebraic framework, the symmetry principle is still present in a certain form, encompassing in a same object both infinitesimal gauge (internal) transformations and diffeomorphisms of the base manifold. It is possible to define a notion of connection (ordinary and generalized) which can encompass in a natural way the Higgs field and its potential. It is also possible to define a generalized metric on the Lie algebroid which gives a connection (gauge field) and a metric on the base manifold (gravitation). We finally present a current work which allows to write Cartan geometries in the framework of Lie algebroids. We conclude presenting the possible generalizations to which this framework naturally leads us.

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