Solution

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

Both Noether charges require boundary conditions that admit the stated transformations and no net boundary-current flux. Take a sufficiently localized field on the whole rod, with the weighted integrals below finite. Fixed endpoints at finite positions generally spoil the waveform-dilation symmetry.

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