Localization of the number of photons of ground states in nonrelativistic QED

研究成果: ジャーナルへの寄稿記事

6 引用 (Scopus)

抄録

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2(ℝ3) ⊗ F ≅ L2 (ℝ3; F), where F is the Boson Fock space over L2(ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to ∩k = 1 D(1 ⊗ Nk), where N denotes the number operator of F. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ∥(1 ⊗ Nk/2ψg(x)∥F ≤ Dke-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular ψg ∈ ∩k = 1 D(eβ|x|m+1 ⊗ Nk) for 0 < 0 < δ/2 is obtained.

元の言語英語
ページ(範囲)271-312
ページ数42
ジャーナルReviews in Mathematical Physics
15
発行部数3
DOI
出版物ステータス出版済み - 5 1 2003

Fingerprint

radiation distribution
Ground State
Photon
Radiation
Electron
operators
ground state
Fock Space
photons
Self-adjoint Operator
Bosons
Infrared
electrons
cut-off
bosons
Denote
Arbitrary
Operator

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

Localization of the number of photons of ground states in nonrelativistic QED. / Hiroshima, Fumio.

:: Reviews in Mathematical Physics, 巻 15, 番号 3, 01.05.2003, p. 271-312.

研究成果: ジャーナルへの寄稿記事

@article{bfdb97ccd92a480a9b66959df02d3679,
title = "Localization of the number of photons of ground states in nonrelativistic QED",
abstract = "One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2(ℝ3) ⊗ F ≅ L2 (ℝ3; F), where F is the Boson Fock space over L2(ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to ∩k = 1 ∞D(1 ⊗ Nk), where N denotes the number operator of F. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ∥(1 ⊗ Nk/2ψg(x)∥F ≤ Dke-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular ψg ∈ ∩k = 1 ∞D(eβ|x|m+1 ⊗ Nk) for 0 < 0 < δ/2 is obtained.",
author = "Fumio Hiroshima",
year = "2003",
month = "5",
day = "1",
doi = "10.1142/S0129055X03001667",
language = "English",
volume = "15",
pages = "271--312",
journal = "Reviews in Mathematical Physics",
issn = "0129-055X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",

}

TY - JOUR

T1 - Localization of the number of photons of ground states in nonrelativistic QED

AU - Hiroshima, Fumio

PY - 2003/5/1

Y1 - 2003/5/1

N2 - One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2(ℝ3) ⊗ F ≅ L2 (ℝ3; F), where F is the Boson Fock space over L2(ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to ∩k = 1 ∞D(1 ⊗ Nk), where N denotes the number operator of F. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ∥(1 ⊗ Nk/2ψg(x)∥F ≤ Dke-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular ψg ∈ ∩k = 1 ∞D(eβ|x|m+1 ⊗ Nk) for 0 < 0 < δ/2 is obtained.

AB - One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2(ℝ3) ⊗ F ≅ L2 (ℝ3; F), where F is the Boson Fock space over L2(ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to ∩k = 1 ∞D(1 ⊗ Nk), where N denotes the number operator of F. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ∥(1 ⊗ Nk/2ψg(x)∥F ≤ Dke-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular ψg ∈ ∩k = 1 ∞D(eβ|x|m+1 ⊗ Nk) for 0 < 0 < δ/2 is obtained.

UR - http://www.scopus.com/inward/record.url?scp=30244506465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30244506465&partnerID=8YFLogxK

U2 - 10.1142/S0129055X03001667

DO - 10.1142/S0129055X03001667

M3 - Article

AN - SCOPUS:30244506465

VL - 15

SP - 271

EP - 312

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 3

ER -