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Title: Ultraviolet renormalization of the Nelson Hamiltonian through functional integration
Authors: Gubinelli, Massimiliano
Hiroshima, Fumio
Lorinczi, Jozsef
Keywords: Nelson model
Ultraviolet cutoff
Energy renormalization
Feynman–Kac representation
Issue Date: 2014
Publisher: © Elsevier
Citation: GUBINELLI, 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.
Abstract: © 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.
Description: This 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
Version: Accepted for publication
DOI: 10.1016/j.jfa.2014.08.002
URI: https://dspace.lboro.ac.uk/2134/21399
Publisher Link: http://dx.doi.org/10.1016/j.jfa.2014.08.002
ISSN: 0022-1236
Appears in Collections:Published Articles (Maths)

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