arXiv subjects
Publications and source records attributed to C. Gérard.
We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff.
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.