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Perturbative Renormalization in Quantum Mechanics

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arxiv hep-th/9309013 v1 pith:GXUGHHUB submitted 1993-09-02 hep-th

Cristina Manuel , Rolf Tarrach This is my paper · ORCID
classification hep-th
keywords quantumbecauseleadpotentialrelevancerenormalizationusedaharonov-bohm
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Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite physical results, which compare correctly to the exact ones. The Dirac delta potential, because of its relevance to triviality, and the Aharonov-Bohm potential, because ot its relevance to anyons, are used as examples here.

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  1. Probing the Universe's Topology through a Quantum System?

    quant-ph 2025-05 conditional novelty 5.0 of 10

    A toy model shows that cosmic topology alters the bound-state energy of a 3D Dirac delta potential by a coefficient C_Γ=6 for the 3-torus and C_Γ=4 for the half-turn space, suppressed by exp(-L/g_R).

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