  It is generally assumed that quantum field theory (QFT) is gauge invariant.
However it is well known that non-gauge invariant terms appear in various
calculations. This problem was recently examined in [9] for a "simple" field
theory and it was shown that for this case QFT in the Schroedinger picture is
not, in fact, gauge invariant. In order to shed further light on this problem
we will examine the Heisenberg and Schroedinger formulations of QFT. It is
generally assumed that these two "pictures" are equivalent; however we will
show that this is not necessarily the case. We shall consider a simple field
theory consisting of a quantized fermion field in the presence of a classical
electromagnetic field. We will show that, although the two pictures are
formally equivalent, the Heisenberg picture is gauge invariant but that the
Schroedinger picture is not. This suggests that the proper way to formulate QFT
is to use the Heisenberg picture.
