Natural Symmetries of the Yang-Mills Equations

Details Natural Symmetries of the Yang-Mills Equations Natural Symmetries of the Yang-Mills Equations

1994-07-20

arxiv.org/abs/hep-th/9407129v1

J.Math.Phys. 36 (1995) 2113-2130

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, plain TeX

Scientific paper

10.1063/1.531103

We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang-Mills connections we introduce a spinorial coordinate system that is adapted to the solution subspace defined by the Yang-Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a straightforward manner. We find that all natural symmetries of the Yang-Mills equations stem from the gauge transformations admitted by the equations.

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