On Quantum Dynamics on C*-Algebras

We consider the problem of constructing quantum dynamics for symmetric Hamiltonian operators that have no self-adjoint extensions. For an earlier studied model, it was found that an elliptic self-adjoint regularization of a symmetric Hamiltonian operator allows one to construct quantum dynamics for vector states on certain C*-subalgebras of the algebra of bounded operators in a Hilbert space. In the present study, we prove that one can extend the dynamics to arbitrary states on these C*-subalgebras while preserving the continuity and convexity. We show that the obtained extension of the dynamics of the set of states on C*-subalgebras is the limit of a sequence of regularized dynamics under removal of the elliptic regularization. We also analyze the properties of the limit dynamics of the set of states on the C*-subalgebras.