1306.0812 (Dan Solomon)

Second quantization and gauge invariance    [PDF]

Dan Solomon

It is well know 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.

View original: http://arxiv.org/abs/1306.0812