Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Massimiliano Gubinelli, Fumio Hiroshima, József Lorinczi

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3125-3153
Number of pages29
JournalJournal of Functional Analysis
Volume267
Issue number9
DOIs
Publication statusPublished - Nov 1 2014

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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

In: Journal of Functional Analysis, Vol. 267, No. 9, 01.11.2014, p. 3125-3153.

Research output: Contribution to journalArticle

Gubinelli, Massimiliano ; Hiroshima, Fumio ; Lorinczi, József. / Ultraviolet renormalization of the Nelson Hamiltonian through functional integration. In: Journal of Functional Analysis. 2014 ; Vol. 267, No. 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 -