Infrared problem for the Nelson model on static space-times
Mathematical Physics
2015-05-18 v3 math.MP
Abstract
We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. 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. A physical example is obtained by quantizing the Klein-Gordon equation on a static space-time coupled with a non-relativistic particle. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass tends to 0 at infinity.
Cite
@article{arxiv.1004.5204,
title = {Infrared problem for the Nelson model on static space-times},
author = {Christian Gérard and Fumio Hiroshima and Annalisa Panati and Akito Suzuki},
journal= {arXiv preprint arXiv:1004.5204},
year = {2015}
}