Lie Algebroid Yang Mills with Matter Fields

Details Lie Algebroid Yang Mills with Matter Fields Lie Algebroid Yang Mills with Matter Fields

2009-08-21

arxiv.org/abs/0908.3161v1

J.Geom.Phys.59:1613-1623,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, accepted for publication in J. Geom. Phys

Scientific paper

10.1016/j.geomphys.2009.07.018

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie algebroid connection. The presentation is kept in part explicit so as to be accessible also to a less mathematically oriented audience.

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