2001/10/31 by Horacio E. Camblong, Carlos Ordońẽz, Carlos R. Ordonez · 2 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Chromodynamics and Particle Interactions #Quantum, superfluid, helium dynamics #hep-ph #hep-th #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1103/physreva.65.052123
published as Phys.Rev. A65 (2002) 052123 · 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchanged
openalex publication_date 2002/05/17 · arxiv created 2002/05/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A path-integral approach for \ensuremathδ-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale-invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the \ensuremathδ-function bound state. The well-known singular character of the two-dimensional \ensuremathδ-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.