  While non-action generated, but identically conserved,-abelian and non-gauge
vectors exist, they are unsuitable for building alternate field equations
because they have no stress-tensor, hence do not permit Poincare generators
and, most phiyically, cannot couple consistently to gravity. Separately, their
geometric analogues -covariantly conserved non-Lagrangian symmetric
tensors-probably do not exist, but their weak field, abelian counterparts do,
and share the vector fields' absence of generators.
