Natural Symmetries of the Yang-Mills Equations

Abstract

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 Poincaré 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.

23 pages, plain TeX

References in corpus (2)

• Classification of Generalized Symmetries for the Vacuum Einstein Equations
• Symmetries of the Einstein Equations

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• Gauge theories of spacetime symmetries
• Deformations of vector-scalar models
• Geometrical representation of Euclidean general relativity in the canonical formalism
• Aspects of electric-magnetic dualities in maximal supergravity
• Lie Symmetries of the Self-Dual Yang-Mills Equations
• String Dualities and Gaugings of Supergravity
• Classification of generalized symmetries of the Yang-Mills fields with a semi-simple structure group