Freedom to choose the gauge

In theories that are gauge invariant we are free either to try to work in a manifestly gauge-invariant fashion, or, since it cannot affect the final physical results, to choose a convenient gauge in which to work. In classical electrodynamics one often uses the Lorentz gauge in which 

This makes Maxwell s equations look simple. In quantum field theory things are more complicated because equations like (2.4.1), if interpreted literally as equations for the field operators, sometimes contradict the fundamental commutation relations that the fields must satisfy. Another common choice in QED is to have 

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