Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Massimiliano Gubinelli, Fumio Hiroshima, József Lorinczi

Research output: Contribution to journalArticlepeer-review

10 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

All Science Journal Classification (ASJC) codes

  • Analysis

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