Operators fields and classical fields

[quantumfireball]

Whats the intuition behind the concept of current operator in QFT and PP.
For example i know that the charge operaor which correspond to space integral of J-o
when acted upon a fock space of the field of given type gives the total charge in the field
but what about the remaining components ,how to intepret them?


NB: Plz forgive me for being a MORON

 

[blechman]

It is exactly the same as the classical current operator - it represents the flow of charge:

$$J^0\sim\rho$$
$$J^i\sim\rho v^i$$