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

摘要

In this short article, we non-perturbatively derive a recursive formula forthe Green's function associated with finitely many point Dirac delta potentialsin one dimension. We also extend this formula to the case for the Dirac deltapotentials supported by regular curves embedded in two dimensional manifoldsand for the Dirac delta potentials supported by two dimensional compactmanifolds embedded in three dimensional manifolds. Finally, this formulationallows us to find the recursive formula of the Green's function for the pointDirac delta potentials in two and three dimensional Riemannian manifolds, wherethe renormalization of coupling constant is required.