Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

  title={Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit},
  author={Michele Correggi and Marco Falconi},
  journal={Annales Henri Poincar{\'e}},
We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding degrees of freedom are traced out, the effective Hamiltonian of the particles converges in resolvent sense to a self-adjoint Schrödinger operator with an additional potential, depending on the state of the field. Moreover, we explicitly derive the expression of such a… 

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