1304.6662 (M. Gubinelli et al.)

Ultraviolet Renormalization of the Nelson Hamiltonian through Functional
Integration    [PDF]

M. Gubinelli, F. Hiroshima, J. Lorinczi

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.

View original: http://arxiv.org/abs/1304.6662