The Helmholtz theorem guarantees that the vector potential can be decomposed in the form A = A
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The Helmholtz theorem guarantees that the vector potential can be decomposed in the form A = A⊥ + AІІ where ∇ · A⊥ = 0 and ∇ × A = 0. Show that a gauge invariant physical observable can be expressed in terms of A⊥, but not AІІ.
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