抄録
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)≤Cx-μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.
| 元の言語 | 英語 |
|---|---|
| ページ（範囲） | 273-299 |
| ページ数 | 27 |
| ジャーナル | Journal of Functional Analysis |
| 巻 | 262 |
| 発行部数 | 1 |
| DOI | |
| 出版物ステータス | 出版済み - 1 1 2012 |
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All Science Journal Classification (ASJC) codes
- Analysis
これを引用
Absence of ground state for the Nelson model on static space-times. / Gérard, C.; Hiroshima, Fumio; Panati, A.; Suzuki, A.
：: Journal of Functional Analysis, 巻 262, 番号 1, 01.01.2012, p. 273-299.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - Absence of ground state for the Nelson model on static space-times
AU - Gérard, C.
AU - Hiroshima, Fumio
AU - Panati, A.
AU - Suzuki, A.
PY - 2012/1/1
Y1 - 2012/1/1
N2 - 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)≤Cx-μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.
AB - 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)≤Cx-μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.
UR - http://www.scopus.com/inward/record.url?scp=80955158382&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80955158382&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2011.09.010
DO - 10.1016/j.jfa.2011.09.010
M3 - Article
VL - 262
SP - 273
EP - 299
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -