Momentum approach to the $1/r^2$ potential as a toy model of the Wilsonian renormalization

Abstract

The Bessel operator, that is, the Schrödinger operator on the half-line with a potential proportional to $1/x^2$, is analyzed in the momentum representation. Many features of this analysis are parallel to the approach à la K. Wilson to Quantum Field Theory: one needs to impose a cutoff, add counterterms, study the renormalization group flow with its fixed points and limit cycles.

References in corpus (4)

• Renormalization of Singular Potentials and Power Counting
• On Schroedinger operators with inverse square potentials on the half-line
• Renormalization group procedure for potential $-g/r^2$
• Topological Levinson's theorem for inverse square potentials: complex, infinite, but not exceptional

Cited by in corpus (1)

• Schrödinger operators with multiple Aharonov-Bohm fluxes