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Lie algebroid Yang-Mills with matter fields. (English) Zbl 1177.53024
Summary: 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 explicit in part so as to be also accessible to a less mathematically oriented audience.

MSC:
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
58H05 Pseudogroups and differentiable groupoids
81T13 Yang-Mills and other gauge theories in quantum field theory
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
53C80 Applications of global differential geometry to the sciences
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References:
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