  A scalar quantum field model defined on a pseudo Riemann manifold is
considered. The model is unitarily transformed the one with a variable mass. By
means of a Feynman-Kac-type formula, it is shown that when the variable mass is
short range, the Hamiltonian has no ground state. Moreover the infrared
divergence of the expectation values of the number of bosons in the ground
state is discussed.
