TY - JOUR

T1 - Absence of ground state for the Nelson model on static space-times

AU - Gérard, C.

AU - Hiroshima, F.

AU - Panati, A.

AU - Suzuki, A.

N1 - Funding Information:
F.H. acknowledges support of Grant-in-Aid for Science Research (B) 20340032 from JSPS and Grant-in-Aid for Challenging Exploratory Research 22654018 from JSPS, and is thankful to the hospitality of Université de Paris XI, where part of this work has been done.

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.

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U2 - 10.1016/j.jfa.2011.09.010

DO - 10.1016/j.jfa.2011.09.010

M3 - Article

AN - SCOPUS:80955158382

VL - 262

SP - 273

EP - 299

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -