  Quantum field theory is assumed to be gauge invariant. However it is well
known that when certain quantities, such as the vacuum current, are calculated
the results are not gauge invariant. The non-gauge invariant terms have to be
removed in order to obtain a physically correct result. It has been shown in
Ref. [3] and [4] that this problem may be due to a mathematical inconsistency
in the canonical formulation of QFT. In this article we will review this
previous work and then examine an alternative formulation of QFT called the
functional Schroedinger approach. It will be shown that this approach produces
different results then the canonical formulation. In particular it will be
shown that in the functional Schroedinger approach the vacuum current is gauge
invariant.

Quantum Physics