Existence of the ground state for the Pauli-Fierz model with a variable mass

Abstract

The Pauli-Fierz model with a variable mass $v$ is considered. An ultraviolet cutoff and an infrared regularity condition are imposed on a quantized radiation field. It is shown that the ground state exists for arbitrary values of coupling constants, when $v(x)\leq c\langle x\rangle^{-\beta}$, $\beta>3$.