 Uniform field shift

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2017/1/b/uniform-field-shift

The transformation

ψ \mapsto ψ + b

j_{1}^{0} = A ρ \dot{ψ} = Π, j_{1}^{z} = - A K ψ^{'}, Q_{1} = \int_{- \infty}^{\infty} Π d z .

Its divergence vanishes by the equation of motion. The charge is the total longitudinal mechanical momentum to this order in the displacement field.

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