Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Massimiliano Gubinelli, Fumio Hiroshima, József Lorinczi

研究成果: ジャーナルへの寄稿記事

7 引用 (Scopus)

抄録

Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.

元の言語英語
ページ(範囲)3125-3153
ページ数29
ジャーナルJournal of Functional Analysis
267
発行部数9
DOI
出版物ステータス出版済み - 11 1 2014

Fingerprint

Functional Integration
Ultraviolet
Renormalization
Gibbs Measure
Weak Coupling
Term
Self-adjoint Operator
Interaction

All Science Journal Classification (ASJC) codes

  • Analysis

これを引用

Ultraviolet renormalization of the Nelson Hamiltonian through functional integration. / Gubinelli, Massimiliano; Hiroshima, Fumio; Lorinczi, József.

:: Journal of Functional Analysis, 巻 267, 番号 9, 01.11.2014, p. 3125-3153.

研究成果: ジャーナルへの寄稿記事

Gubinelli, Massimiliano ; Hiroshima, Fumio ; Lorinczi, József. / Ultraviolet renormalization of the Nelson Hamiltonian through functional integration. :: Journal of Functional Analysis. 2014 ; 巻 267, 番号 9. pp. 3125-3153.
@article{64f7a37d136042049480ad6558dab165,
title = "Ultraviolet renormalization of the Nelson Hamiltonian through functional integration",
abstract = "Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.",
author = "Massimiliano Gubinelli and Fumio Hiroshima and J{\'o}zsef Lorinczi",
year = "2014",
month = "11",
day = "1",
doi = "10.1016/j.jfa.2014.08.002",
language = "English",
volume = "267",
pages = "3125--3153",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "9",

}

TY - JOUR

T1 - Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

AU - Gubinelli, Massimiliano

AU - Hiroshima, Fumio

AU - Lorinczi, József

PY - 2014/11/1

Y1 - 2014/11/1

N2 - Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.

AB - Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.

UR - http://www.scopus.com/inward/record.url?scp=85027955733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027955733&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2014.08.002

DO - 10.1016/j.jfa.2014.08.002

M3 - Article

AN - SCOPUS:85027955733

VL - 267

SP - 3125

EP - 3153

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 9

ER -