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Pré-Publication, Document De Travail Année : 2016

Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model

Résumé

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 Schr\"odinger-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.

Dates et versions

hal-01280574 , version 1 (29-02-2016)

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Zied Ammari, Marco Falconi. Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model. 2016. ⟨hal-01280574⟩
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