  We calculate the lowest Landau level (LLL) current by working in the full
Hilbert space of a two dimensional electron system in a magnetic field and
keeping all the non-vanishing terms in the high field limit. The answer a) is
not represented by a simple LLL operator and b) differs from the current
operator, recently derived by Martinez and Stone in a field theoretic LLL
formalism, by solenoidal terms. Though that is consistent with the inevitable
ambiguities of their Noether construction, we argue that the correct answer
cannot arise naturally in the LLL formalism.
