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In the mid Sixties Edward Nelson proved the existence of a consistent quantumfield theory that describes the Yukawa-like interaction of a non-relativisticnucleon field with a relativistic meson field. Since then it is thought,despite the renormalization procedure involved in the construction, that thequantum dynamics should be governed in the classical limit by aSchr\"odinger-Klein-Gordon system with Yukawa coupling. In the present paper weprove this fact in the form of a Bohr correspondence principle. Besides, ourresult enlighten the nature of the renormalization method employed in thismodel which we interpret as a strategy that allows to put the related classicalHamiltonian PDE in a normal form suitable for a canonical quantization.

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