Infrared problem for the Nelson model on static space-times. (English) Zbl 1269.83036
Summary: 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 \(m(x) \geq C |x|^{-1}\) at infinity for some \(C > 0\) then the Nelson Hamiltonian has a ground state.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83A05 | Special relativity |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 80A10 | Classical and relativistic thermodynamics |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81V17 | Gravitational interaction in quantum theory |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
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