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Article Dans Une Revue Journal of Geometry and Physics Année : 2013

Formulation of gauge theories on transitive Lie algebroids

Résumé

In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration along the algebraic part of the transitive Lie algebroid (its kernel). Explicit action functionals are given in terms of global objects and in terms of their local description as well. We investigate applications of these constructions to Atiyah Lie algebroids and to derivations on a vector bundle. The obtained gauge theories are discussed with respect to ordinary and to similar non-commutative gauge theories.

Dates et versions

hal-00769444 , version 1 (01-01-2013)

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Cédric Fournel, Serge Lazzarini, Thierry Masson. Formulation of gauge theories on transitive Lie algebroids. Journal of Geometry and Physics, 2013, 64, pp.174. ⟨10.1016/j.geomphys.2012.11.005⟩. ⟨hal-00769444⟩
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