One of the most important symmetries in Nature is that of scale invariance. This symmetry is very
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One of the most important symmetries in Nature is that of scale invariance. This symmetry is very common (e.g. arises whenever a substance undergoes a phase transition), fundamental (e.g. it is at the foundation of the concept of renormalization group for which a physics Nobel Prize was awarded in 1982), and entertaining (as you will now see in this problem).
Consider the action
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