Generalized Proca and its Constraint Algebra
  We reconsider the construction of general derivative self-interactions for a
massive Proca field. The constructed Lagrangian is such that the vector field
propagates at most three degrees of freedom, thus avoiding the ghostly nature
of a fourth polarisation. The construction makes use of the well-known
condition for constrained systems of having a degenerate Hessian. We briefly
discuss the casuistry according to the nature of the existing constraints
algebra. We also explore various classes of interesting new interactions that
have been recently raised in the literature. For the sixth order Lagrangian
that satisfies the constraints by itself we prove its topological character,
making such a term irrelevant. There is however a window of opportunity for
exploring other classes of fully-nonlinear interactions that satisfy the
constraint algebra by mixing terms of various order.
