Second quantization and gauge invariance
Quantum Physics
2013-07-02 v2 Mathematical Physics
math.MP
Abstract
It is well known that the single particle Dirac equation is gauge invariant. This means that observable quantities, such as the current density, are not affected by a gauge transformation. However what happens when the method of second quantization is applied to convert a single particle theory into a field theory? In this case it will be shown that the theory is no longer gauge invariant. This will be shown by considering the second quantization of a zero mass Dirac field in 1+1 dimensions and examining the change of the current density operator due to a gauge transformation.
Cite
@article{arxiv.1306.0812,
title = {Second quantization and gauge invariance},
author = {Dan Solomon},
journal= {arXiv preprint arXiv:1306.0812},
year = {2013}
}
Comments
Added some additional introductory material. Some other minor changes and correction of typos. 10 pages