So I have the following curiosity: Consider for example, in QED, the quantity
$$ j^\mu\equiv\partial_\nu (\lambda(x) F^{\mu \nu}) $$
where $\lambda(x)$ is an arbitrary scalar function of spacetime, constructed from elements of the theory, e.g.
$$ \lambda(x)=A_\mu A^\mu F_{\rho \sigma} F^{\rho \sigma} $$
or anything else you can think of. Then, since $F^{\mu \nu}$ is antisymmetric, $\partial_\mu j^\mu=0$ identically.
In fact this can be generalized to any theory; construct from various elements an antisymmetric two-rank tensor, and a scalar, multiply them together, and there is a corresponding conserved current for any choice you make. If these currents are not trivial (e.g. giving only vanishing charges) then it appears that all theories give an infinite landscape of conserved currents. Is this so? Am I missing something? How is this justified logically?