Classical Higgs fields and related canonical conserved quantities are defined by invariant variational problems on suitably defined gauge gluon bundles. We consider Lagrangian field theories which are assumed to be invariant with respect to the action of a gauge-natural group. As an illustrative example we exploit the 'gluon Lagrangian', i.e. a Yang-Mills Lagrangian on the (1, 1)-order gauge-natural bundle of S U(3)-principal connections. The kernel of the gauge-natural Jacobi morphism for such a Lagrangian, by inducing a reductive split structure, canonically defines a 'gluon classical Higgs field'.
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