Existence of a Unique Local Solution to the Many-body Maxwell-Schr'odinger Initial Value Problem

摘要

We study the many-body problem of charged particles interacting with theirself-generated electromagnetic field. We model the dynamics of the particles bythe many-body Maxwell-Schr\"odinger system, where the particles are treatedquantum mechanically and the electromagnetic field is a classical quantity. Weprove the existence of a unique local in time solution to this nonlinearinitial value problem using a contraction mapping argument.