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We consider the Nelson model with variable coefficients and investigate theproblem of existence of a ground state and the removal of the ultravioletcutoff. Nelson models with variable coefficients arise when one replaces in theusual Nelson model the flat Minkowski metric by a static metric, allowing alsothe boson mass to depend on position. A physical example is obtained byquantizing the Klein-Gordon equation on a static space-time coupled with anon-relativistic particle. We investigate the existence of a ground state ofthe Hamiltonian in the presence of the infrared problem, i.e. assuming that theboson mass tends to 0 at infinity.

Infrared problem for the Nelson model on static space-times