Operators fields and classical fields

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The discussion focuses on the intuition behind the current operator in Quantum Field Theory (QFT) and its relation to classical fields. The charge operator, which corresponds to the spatial integral of the time component of the current density, provides the total charge in a given field when applied to Fock space. Participants clarify that the remaining components of the current operator can be interpreted similarly to classical physics, where the time component represents charge density and spatial components represent charge flow. The analogy emphasizes that the current operator in QFT mirrors classical current behavior, linking charge density to its flow. Understanding these relationships enhances comprehension of how quantum operators function in field theory.
quantumfireball
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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
 
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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
 

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