For a massive vector boson field: (a) Prove Eq. (6.5.51), which is the result that (hat{A}^{0}(x)=-boldsymbol{abla} cdot

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For a massive vector boson field:

(a) Prove Eq. (6.5.51), which is the result that \(\hat{A}^{0}(x)=-\boldsymbol{abla} \cdot \hat{\mathbf{E}}(x) / m^{2}\) for a free massive vector boson field.

(b) Prove Eq. (6.5.54), which are the commutation relations for the annihilation and creation operators.

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