Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

Details Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

2001-10-19

arxiv.org/abs/hep-th/0110176v4

Phys.Rev. A65 (2002) 052123

Physics

High Energy Physics

High Energy Physics - Theory

26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and

Scientific paper

10.1103/PhysRevA.65.052123

A path-integral approach for delta-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 delta-function bound state. The well-known singular character of the two-dimensional delta-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.

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