Classical-Quantum motion of charged particles in interaction with scalar field.

 

 

 

This talk explores the quantum-classical transition in particle-field dynamics where a finite and fixed number of non-relativistic or semi-relativistic quantum particles interact with a quantized scalar field in the scaling limit of small value of Planck constant $\hbar\to 0$. Such topic aims to rigorously derive effective equations from fundamental first principles of quantum mechanics. In our case, the interaction between the wave and the particles are sufficiently singular to prevent us from using a standard fixed point argument. So that, when analyzing the quantum-classical transition, we crucially use the transferring of some a priori quantum regularizing effects to the classical equation in such a way that we are able to establish the global well-posedness for the particle-field equation while studying the transition by means of Wigner measures. And at the same time, we establish the Bohr’s correspondence principle.