Formulation of gauge theories on transitive Lie algebroids

JOURNAL OF GEOMETRY AND PHYSICS

卷:64

Article

Fournel, Cedric¹  Lazzarini, Serge¹  Masson, Thierry¹ 

[1] CNRS Marseille Luminy, Ctr Phys Theor, F-13288 Marseille 9, France

关键词: Differential geometry;    Differential algebra;    Lie algebroid;    Gauge theories;    Yang-Mills-Higgs models;   

DOI  :  10.1016/j.geomphys.2012.11.005

来源: Elsevier

【 摘 要 】

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 noncommutative gauge theories. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free