Dynamics of virtual bosons created by classical and quantum sources

We use the Yukawa model of interacting photons and fermions to study the dynamics of the creation of a virtual photon cloud around a spatially localized bare fermion. The temporal evolution of the photons’ spatial probability density is characterized by three stages, the shape-invariant growth, the spreading, and finally the formation of a steady state. Exactly half of the total number of created photons escape irreversibly while the other half remains in the vicinity of the fermion. For the special case of an infinitely narrow fermion distribution the product of the fermionic field operators in the interaction Hamiltonian can be replaced by a simple classical mechanical density, thus eliminating all fermionic degrees of freedom. We examine the effects of quantum mechanics on the total number of photons created by a spatially extended fermion.