Ultraviolet renormalization of the Nelson Hamiltonian through functional integration

Gubinelli, Massimiliano; Lorinczi, József; Hiroshima, Fumio

Gubinelli, Massimiliano; Lorinczi, József; Hiroshima, Fumio (2014), Ultraviolet renormalization of the Nelson Hamiltonian through functional integration, Journal of Functional Analysis, 267, 9, p. 3125-3153. http://dx.doi.org/10.1016/j.jfa.2014.08.002

Type

Article accepté pour publication ou publié

Date

2014

Journal name

Journal of Functional Analysis

Volume

267

Number

Publisher

Academic Press

Pages

3125-3153

Abstract (EN)

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.

Subjects / Keywords

Nelson model; Ultraviolet cutoff; Feynman–Kac representation; Energy renormalization