Document Type

Article

Publication Date

5-17-2002

Abstract

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

Comments

Article publihsed in Physical Review A, 65, pp 052123 (2002).

© 2002 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.65.052123

DOI: 10.1103/PhysRevA.65.052123

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