Burak Kaynak, Bogazici University
The relativistic Lee model on Riemannian manifolds
We study the relativistic Lee model on static Riemannian manifolds.
The model is constructed nonperturbatively through its resolvent,
which is based onthe 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 is 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 the
(2 + 1)-dimensional model.