Prove using the definitions (27.16) that Eq. (27.15) is equivalent to Eq. (27.17), which has the form

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Prove using the definitions (27.16) that Eq. (27.15) is equivalent to Eq. (27.17), which has the form of a gauge coupling to a vector potential \(\boldsymbol{A}_{n}(\boldsymbol{R})\).

Data from Eq. 27.15

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Data from Eq. 27.16

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Data from Eq. 27.17

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