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Gauge theory on a fibred manifold. (English) Zbl 0824.53024

The author describes a gauge theory for applications to multidimensional physical theories.
Fixed a fibred manifold \(N\), he considers a horizontal distribution \(H\) on \(N\) and develops a related tensor calculus defining also a covariant derivative on depending on the distribution \(H\) and on two linear connections on the horizontal and vertical vector bundles. Then, he obtains the conservation laws for Lagrangians invariant with respect to the global action of a real Lie group, and describes the minimal replacement in order to get a local gauge invariant Lagrangian from a global gauge invariant one.
Furthermore, he constructs the Lagrangians for horizontal and vertical gauge fields and obtains the equations of motion, the conservation laws and the Bianchi identities.
Reviewer: A.M.Pastore (Bari)

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T13 Yang-Mills and other gauge theories in quantum field theory
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