The conserved current in KG is

$$j^{\mu}=i(\phi^*\partial^{\mu}\phi-\phi\partial^{\mu}\phi^*) =2p^{\mu}|N|^2$$

where N is a normalization factor. This current can't be understood as a probability current because $j^0$ can be negative. This problem is solved thinking of $j^{\mu}$ as a charge current and not probability. Then negative and positive energy solutions have opposite charges.

On the other hand, the conserved current in Dirac equation is


which is definite positive. This is okay because we think of this current, again, as a probability current.

Which is the correct interpretation? are conserved currents of classical equations charge currents or probability currents? Is this solved in any way in QFT?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.