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arXiv · 1304.6662

Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration

M. Gubinelli·F. Hiroshima·J. Lorinczi
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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.

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M. Gubinelli, F. Hiroshima, J. Lorinczi. 2013-10-04. Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration. https://arxiv.org/abs/1304.6662

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