On the Inequivalence of Renormalization and Self-Adjoint Extensions for Quantum Singular Interactions
arXiv:hep-th/0604018 · doi:10.1016/j.physleta.2006.12.041
Abstract
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
19 pages, including 2 figures. The title and abstract were changed to more accurately reflect the content. The text was rearranged into sections, with several equations and multiple paragraphs added for clarity; and a few typos were corrected. The central equations and concepts remain unchanged.
References in corpus (4)
Cited by in corpus (4)
- Renormalization of Singular Potentials and Power Counting
- Polymer quantization, singularity resolution and the 1/r^2 potential
- Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
- J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory