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 halfline 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.