  We study the interaction of mutually non-interacting Klein-Gordon particles
with localized sources on stochastically complete Riemannian surfaces. This
asymptotically free theory requires regularization and coupling constant
renormalization. Renormalization is performed non-perturbatively using the
orthofermion algebra technique and the principal operator $\Phi$ is found. The
principal operator is then used to obtain the bound state spectrum, in terms of
binding energies to single Dirac-delta function centers. The heat kernel method
allows us to generalize this procedure to compact and Cartan-Hadamard type
Riemannian manifolds. We make use of upper and lower bounds on the heat kernel
to constrain the ground state energy from below thus confirming that our
neglect of pair creation is justified for certain ranges of parameters in the
problem.
