Time reversal and parity breaking by propagation

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.