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

Abstract

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 Schrödinger-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.

73 pages

References in corpus (2)

• Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors
• Classical limit of the Nelson model with cut off

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• Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
• Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian
• Feynman-Kac formulas for the ultra-violet renormalized Nelson model
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Mean-field limits of particles in interaction with quantized radiation fields
• On the uniqueness of probability measure solutions to Liouville's equation of Hamiltonian PDEs