Bohr's correspondence principle for the renormalized Nelson model


SIAM J. Math. Anal. 49(6), 5031-5095 (2017)

The article is available at SIAM Library (under subscritpion).

arXiv 1602.03212

The preprint in pdf is available at The preprint contains an additional section on the renormalization by means of the classical dressing.


The bibtex entry for the article can be downloaded here.


In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a relativistic meson field. Since then it is thought, despite the renormalization procedure involved in the construction, that the quantum dynamics should be governed in the classical limit by a Schroedinger-Klein-Gordon system with Yukawa coupling. In the present paper we prove this fact in the form of a Bohr correspondence principle. Besides, our result enlighten the nature of the renormalization method employed in this model which we interpret as a strategy that allows to put the related classical Hamiltonian PDE in a normal form suitable for a canonical quantization.