2013/06/03 by Dan Solomon, Solomon, Dan
Medicine · Physics and Astronomy · #Medical Imaging Techniques and Applications #Crystallography and Radiation Phenomena #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1306.0812
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.