Formulation of gauge theories on transitive Lie algebroids

Abstract

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.

arXiv comment30 pages. Final version. arXiv admin note: substantial text overlap with arXiv:1109.4282

References in corpus (3)

• Connections on Lie algebroids and on derivation-based noncommutative geometry
• On the Noncommutative Geometry of the Endomorphism Algebra of a Vector Bundle
• Noncommutative generalization of SU(n)-principal fiber bundles: a review

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