Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces

Abstract

In this short article, we nonperturbatively derive a recursive formula for the Green's function associatedwith nitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Diracdelta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentialssupported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulationallows us to nd the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.