We reconsider the quantum mechanics of scale-invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We argue that the breaking of scale invariance reported in the literature for the δ(r) potential is an example of explicit symmetry breaking and not an anomaly or quantum mechanical symmetry breaking.
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March 01 1998
On scale invariance and anomalies in quantum mechanics
J. L. Lucio;
A. Cabo, J. L. Lucio, H. Mercado; On scale invariance and anomalies in quantum mechanics. Am. J. Phys. 1 March 1998; 66 (3): 240–246. https://doi.org/10.1119/1.18852
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