Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590849 | Journal of Functional Analysis | 2012 | 27 Pages |
Abstract
We consider the Nelson model on some static space–times and investigate the problem of absence of a ground state. 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 investigate the absence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass m(x) tends to 0 at spatial infinity. Using path space techniques, we show that if m(x)⩽C|x|−μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.
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