e scalar and vector potential given by A → A + ∇ψ(r, t) φ → φ − (1/c) (∂ψ/∂t) , where ψ is arbitrary (but differentiable). What effect does this gauge transformation have on the Lagrangian of a particle moving in the electromagnetic field? Is the motion affected?

e scalar and vector potential given by A → A + ∇ψ(r, t) φ → φ − (1/c) (∂ψ/∂t) , where ψ is arbitrary (but differentiable). What effect does this gauge transformation have on the Lagrangian of a particle moving in the electromagnetic field? Is the motion affected?

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[General Theory of Relativity]
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