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Partially classical limit of the Nelson model

J. Ginibre·F. Nironi·G. Velo
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Abstract

We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a situation where the number of Bose excitations becomes infinite while the coupling constant tends to zero in a suitable sense. In that limit the appropriately rescaled Bose field converges to a classical solution of the free wave or Klein-Gordon equation depending on whether the mass of the field is zero or not, the quantum fluctuations around that solution satisfy the wave or Klein-Gordon equation and the evolution of the nonrelativistic particles is governed by a quantum dynamics with an external potential given by the previous classical solution.

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J. Ginibre, F. Nironi, G. Velo. 2004-11-12. Partially classical limit of the Nelson model. https://arxiv.org/abs/math-ph/0411046

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