Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590042 | Journal of Functional Analysis | 2014 | 29 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Massimiliano Gubinelli, Fumio Hiroshima, József Lőrinczi,