Non-relativistic Lee Model in Three Dimensional Riemannian Manifolds

In this work, we construct the non-relativistic Lee model on some class of three dimensional Riemannian manifolds by following a novel approach introduced by S. G. Rajeev [1]. This approach together with the help of heat kernel allows us to perform the renormalization non-perturbatively and explicitly. For completeness, we show that the ground state energy is bounded from below for different classes of manifolds, using the upper bound estimates on the heat kernel. Finally, we apply a kind of mean field approximation to the model for compact and non-compact manifolds separately and discover that the ground state energy grows linearly with the number of bosons n.