Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration

M. Gubinelli, F. Hiroshima and J. Lorinczi

First issued 24 April 2013 · PDF

Abstract

Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the zero 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.

Versions

1. Version 2 (arXiv v2) current
   4 October 2013
   arXiv comments: 28 pages, revision of section 2 and typos corrected
   PDF · LaTeX source · files and digests · arXiv:1304.6662
2. Version 1 (arXiv v1)
   24 April 2013
   arXiv comments: 27 pages
   PDF · LaTeX source · files and digests · arXiv:1304.6662

Cite

M. Gubinelli, F. Hiroshima and J. Lorinczi. Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration. Papers of Massimiliano Gubinelli, 2013, version 2. https://mgubi.org/papers/paper/nelson-uv-renormalisation/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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