# Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Massimiliano Gubinelli, Fumio Hiroshima, József Lorinczi

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 3125-3153 29 Journal of Functional Analysis 267 9 https://doi.org/10.1016/j.jfa.2014.08.002 出版済み - 11 1 2014

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