Abstract
We consider the Nelson model on some static space-times and investigate the problem of existence 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 existence 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. We show that if m(x) ≥ C {pipe}x{pipe}-1 at infinity for some C > 0 then the Nelson Hamiltonian has a ground state.
Original language | English |
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Pages (from-to) | 543-566 |
Number of pages | 24 |
Journal | Communications in Mathematical Physics |
Volume | 308 |
Issue number | 2 |
DOIs | |
Publication status | Published - Dec 2011 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics