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Abstract: It is generally assumed that quantum field theory QFT is gauge invariant.However it is well known that non-gauge invariant terms appear in variouscalculations. This problem was recently examined in 9 for a -simple- fieldtheory and it was shown that for this case QFT in the Schroedinger picture isnot, in fact, gauge invariant. In order to shed further light on this problemwe will examine the Heisenberg and Schroedinger formulations of QFT. It isgenerally assumed that these two -pictures- are equivalent; however we willshow that this is not necessarily the case. We shall consider a simple fieldtheory consisting of a quantized fermion field in the presence of a classicalelectromagnetic field. We will show that, although the two pictures areformally equivalent, the Heisenberg picture is gauge invariant but that theSchroedinger picture is not. This suggests that the proper way to formulate QFTis to use the Heisenberg picture.



Author: Dan Solomon

Source: https://arxiv.org/







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