Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Massimiliano Gubinelli, Fumio Hiroshima, József Lorinczi

研究成果: Contribution to journalArticle査読

10 被引用数 (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.

本文言語英語
ページ(範囲)3125-3153
ページ数29
ジャーナルJournal of Functional Analysis
267
9
DOI
出版ステータス出版済み - 11 1 2014

All Science Journal Classification (ASJC) codes

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