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 two-level system when a t-violating term is added to a t-preserving unperturbed Hamiltonian. Transition probabilities are calculated; moreover, the time evolution of a complex state is determined analytically, showing that a quaternionic component arises naturally in its evolution. Finally, some properties of the time-reversal observable are studied and a set of selection rules is obtained.