  We present a simple recipe to construct the Green's function associated with
a Hamiltonian of the form H=H_0+V, where H_0 is a Hamiltonian for which the
associated Green's function is known and V is a delta-function potential. We
apply this result to the case in which H_0 is the Hamiltonian of a free
particle in D dimensions. Field theoretic concepts such as regularization,
renormalization, dimensional transmutation and triviality are introduced
naturally in order to deal with an infinity which shows up in the formal
expression of the Green's function for D>1.
