The Noether current for a set of scalar fields φa can classically be written as:
jμ(x)=δL(x)∂(∂μφa(x))δφa(x)
The divergence of this current can then be written as: ∂μjμ(x)=δL(x)−δSδφa(x)δφa(x)
If the classical field equations are satisfied the second term on the right hand side vanishes. However in quantum theory the classical field equations are not satisfied. Why is the current still conserved for a symmetry in this case?
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