New developments in the study of Time as a quantum observable

In this brief review, some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the hermitian (more precisely, maximal hermitian, but non-selfadjoint) operator for Time which appears: (i) for particles, in ordinary non-relativistic quantum mechanics; and (ii) for photons (i.e., in first-quantization quantum electrodynamics). On the basis of our unified time analysis of photon and nonrelativistic particle one can, e.g., introduce self-consistent definitions of the tunnelling times, within conventional quantum mechanics (or one-dimensional quantum electrodynamics) only. Besides the countinuous, also the case of discrete energy spectra is investigated, At last, by the introduction of a Time-"Hamiltomian", a new, dual hamiltonian formalism is proposed.