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Communications in Mathematical Physics

, Volume 68, Issue 1, pp 45–68 | Cite as

The classical field limit of scattering theory for non-relativistic many-boson systems. II

  • J. Ginibre
  • G. Velo
Article

Abstract

We study the classical field limit of non relativistic many-boson theories in space dimensionn≧3, extending the results of a previous paper to more singular interactions. We prove the expected results: when ħ tends to zero, the quantum theory tends in a suitable sense to the corresponding classical field theory, and the quantum fluctuations are governed by the equation obtained by linearizing the quantum evolution equation around the classical solution. These results hold uniformly in time and therefore apply to scattering theory. The interactions considered here are so singular as to require a change of domain in order to define the generator of the evolution of the fluctuations, but sufficiently regular so that no energy renormalization is needed.

Keywords

Neural Network Statistical Physic Field Theory Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • J. Ginibre
    • 1
  • G. Velo
    • 2
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité de Paris-SudOrsayFrance
  2. 2.Istituto di Fisica A. RighiUniversità di Bologna, and INFN, Sezione di BolognaI-BolognaItaly

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