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Ultraviolet renormalization of the Nelson Hamiltonian through functional integration
journal contributionposted on 2016-05-27, 14:05 authored by Massimiliano Gubinelli, Fumio Hiroshima, Jozsef Lorinczi
© 2014 Elsevier Inc. 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.
- Mathematical Sciences
Published inJournal of Functional Analysis
Pages3125 - 3153
CitationGUBINELLI, M., HIROSHIMA, F. and LORINCZI, J., 2014. Ultraviolet renormalization of the Nelson Hamiltonian through functional integration. Journal of Functional Analysis, 267(9), pp. 3125-3153.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis paper was accepted for publication in the journal Journal of Functional Analysis and the definitive published version is available at http://dx.doi.org/10.1016/j.jfa.2014.08.002