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It is will known that quantum field theory at the formal level is gaugeinvariant. However a calculation of the vacuum polarization tensor will includenon-gauge invariant terms. These terms must be removed from the calculation inorder to get a physically correct result. One common way to do this today isthe technique of "dimensional regularization". It has recently been noted [2]that at one time a supersymmetric-like solution to the problem was explored -that is, the right combination of fields would cause the offending terms tocancel out. I will examine some of this early work and pose the question - whydo the non-gauge invariant terms appear in the first place? I will show thatthis is due to an improper mathematical step in the formulation of thepertubative expansion. I will then show that when this step is corrected theresult is gauge invariant. However a supersymmetric-like solution is stillrequired to cancel out a divergent term.

Why do non-gauge invariant terms appear in the vacuum polarization tensor?