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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/223364
Singular Potentials and Anomalous Symmetry Breaking
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This work investigates attractive potentials of the form 1/rN for N ≥ 2 in Quantum Mechanics. For the inverse square potential (N = 2) with sufficiently strong coupling, we examine how classical scale symmetry is broken through the renormalization process, representing the simplest example of a quantum anomaly and touching upon the fundamental question of what symmetries are present in reality. This anomaly is exemplified by the existence of a critical dipole moment required to bind an electron to a polar molecule. In contrast, singular potentials with N > 2 exhibit stronger divergences, and we argue why a complete theory cannot be recovered with finitely many parameters, drawing an analogy with nonrenormalizable theories in quantum field theory
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Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2025, Tutor: Tomeu Fiol Núñez
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VEGA CASANOVAS, Andreu. Singular Potentials and Anomalous Symmetry Breaking. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/223364