In quantum electrodynamics problems involving background fields, most text books usually makes the following substitution
Aμ→A′μ=Aμ0+Aμc
Where Ac is classical field satisfying Maxwell equations.
In the path integral formalism this seems reasonable to do since, Aμ0 and Aμc are c numbers but in the canonical formalism Aμ0 are an operator and Aμc a c number.
Is this a reasonable thing to do?
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