Gauge-field transformation law

For

D_{μ} = \partial_{μ} + A_{μ}

and a matter field transforming as

ϕ \mapsto g ϕ

, covariance of

D_{μ} ϕ

requires

A_{μ} \mapsto g A_{μ} g^{- 1} - (\partial_{μ} g) g^{- 1} .

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Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 53 / 4 / Solution
Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 51 / 2 / Solution
Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 302 / 4 / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 302 / 4 / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 302 / 4 / a / Solution

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