Space-time versus particle-hole symmetry of collisions in a non-local kinetic equation for dense Fermi systems

Binary collisions in Fermi systems obey two fundamental symmetries corresponding to the space and time inversion and to the interchange of particles and holes. We show that beyond the local and instant approximation of scattering-in and -out integrals of a kinetic equation, only one of symmetries can be explicit while the other has to be covered by a constraint. This constraint, derived from the optical theorem, allows one to convert at need an explicit particle-hole symmetric form to the space-time symmetric form and vice versa. We implement this constraint to heavy ion reactions, where simulation algorithms require the space-time symmetry while former theories offer kinetic equations with the explicit particle-hole symmetry.