Absence of ground state for the Nelson model on static space-times

C. Gérard, Fumio Hiroshima, A. Panati, A. Suzuki

研究成果: ジャーナルへの寄稿記事

3 引用 (Scopus)

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 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
262
発行部数1
DOI
出版物ステータス出版済み - 1 1 2012

Fingerprint

Ground State
Space-time
Bosons
Infinity
Path Space
Metric
Variable Coefficients
Infrared
Model
Tend

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

Gérard, C. ; Hiroshima, Fumio ; Panati, A. ; Suzuki, A. / Absence of ground state for the Nelson model on static space-times. :: Journal of Functional Analysis. 2012 ; 巻 262, 番号 1. pp. 273-299.
@article{ed533d274bf7417298b220c8860f1562,
title = "Absence of ground state for the Nelson model on static space-times",
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)≤Cx-μ at infinity for some C>0 and μ>1 then the Nelson Hamiltonian has no ground state.",
author = "C. G{\'e}rard and Fumio Hiroshima and A. Panati and A. Suzuki",
year = "2012",
month = "1",
day = "1",
doi = "10.1016/j.jfa.2011.09.010",
language = "English",
volume = "262",
pages = "273--299",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "1",

}

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 -