Time-dependent perturbation theory for quaternionic quantum mechanics, with application toCPnonconservation inK-meson decays

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Abstract
We develop time-dependent perturbation theory for quaternionic quantum mechanics. We set up the analog of the Weisskopf-Wigner formalism for the decay of a degenerate set of states, identify the mass and decay matrices, and verify unitarity. The results support the conjecture that the asymptotic-state structure of quaternionic quantum field theory resides within a complex subspace of quaternionic Hilbert space. With a natural ansatz for the CP behavior of the quaternionic Hamiltonian, the formalism is shown to imply the existence of an effective superweak CP nonconservation in K decays.