Renormalization is applicable in non-relativistic quantum mechanics
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Peer-reviewed literature specifically demonstrates the application and usefulness of renormalization techniques within non-relativistic quantum mechanics and non-relativistic quantum electrodynamics.
The importance and usefulness of renormalization are emphasized in non-relativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin exhibits ultraviolet divergence. The use of renormalization techniques in these problems leads to finite converged results for both the exact and perturbative solutions. The renormalization procedure is carried out for the quantum two-body problem in different partial waves for a minimal potential possessing only the threshold behaviour and no form factors. The renormalized perturbative and exact solutions for this problem are found to be consistent with each other. The useful role of the renormalization group equations for this problem is also pointed out.
Mass Renormalization and Energy Level Shift in Non-Relativistic QED
Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized radiation field. We consider the case of small coupling constant $\alpha$, but fixed $Z\alpha$ and ultraviolet cut-off $\Lambda$. We prove that after renormalizing the mass the binding energy has, to leading order in $\alpha$, a finite limit as $\Lambda$ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of $Z\alpha$, but shows a different behavior for bigger values.
Published as: Adv. Theor. Math. Phys. 6, 847 (2002)
arXiv categories: math-ph math.MP
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