The Nelson model (with ultraviolet cutoff) describes a quantum system of non-relativistic identical particles coupled to a quantized scalar fiel d. In this talk\, I would like to discuss its time evolution in a mean-fie ld limit of many fermions which is coupled to a semiclassical limit. At ti me zero\, we assume that the gauge bosons of the radiation field are in a coherent state and that the state of the fermions is given by a Slater det erminant\, whose reduced one-particle density matrix is an orthogonal proj ection with semiclassical structure. I will motivate that at later times a nd in the limit of many fermions it can be proven that the fermion state r emains close to a slater determinant and that the time evolution is approx imately described by the fermionic Schrö\;dinger-Klein-Gordon equation s. I will introduce the mentioned models and discuss the status and the st ructure of the proof. The talk reports about work in progress with Sö\ ;ren Petrat.

LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS T Austria ORGANIZER:jdeanton@ist.ac.at SUMMARY:Mean-field Dynamics for the Nelson model with Fermions URL:https://talks-calendar.app.ist.ac.at/events/1064 END:VEVENT END:VCALENDAR