  The time independent mean field method (TIMF) for the calculation of matrix
elements of non relativistic propagators is based on a variational principle
whose non linearity induces a multiplicity of variational solutions. Several of
them can break any symmetry shared by the Hamiltonian and initial and final
states. We describe a soluble model where, in particular, time reversal and
parity breakings occur. Such breakings account for important properties of
propagation amplitudes.
