t-violation and quaternionic state oscillations

We derive, using the quaternionic group representation theory, the possible forms of the t-violating Hamiltonians, and consider time evolution in a tw o-level system when a t-violating term is added to a t-preserving unperturb ed Hamiltonian. Transition probabilities are calculated; moreover, the time evolution of a complex state is determined analytically, showing that a qu aternionic component arises naturally in its evolution. Finally, some prope rties of the time-reversal observable are studied and a set of selection ru les is obtained.