  We study the dynamics of an electron wave packet in a strong constant crossed
electromagnetic field with account for radiative corrections due to interaction
of the electron with the vacuum fluctuations. We evaluate a wave packet
composed of the solutions to the Dyson-Schwinger equation, which describes
electron propagation without emission of real photons. Spacetime dependence of
the wave packet is obtained analytically for a short time interval, the more
restricted from above the wider is the packet in momentum space. The radiative
corrections alter the electron wavefunction, resulting in particular in a
damping of the wave packet. The expectation value of the Dirac spin operator
also gets modified.
