  We study the relativistic Lee model on static Riemannian manifolds. The model
is constructed nonperturbatively through its resolvent, which is based on the
so-called principal operator and the heat kernel techniques. It is shown that
making the principal operator well-defined dictates how to renormalize the
parameters of the model. The renormalization of the parameters are the same in
the light front coordinates as in the instant form. Moreover, the
renormalization of the model on Riemannian manifolds agrees with the flat case.
The asymptotic behavior of the renormalized principal operator in the large
number of bosons limit implies that the ground state energy is positive. In 2+1
dimensions, the model requires only a mass renormalization. We obtain rigorous
bounds on the ground state energy for the n-particle sector of 2+1 dimensional
model.
