Cyclotomic Quantum Clock

Time can be defined in many different ways depending on context and discipline.1 In quantum physics its operatorial features that are required by the quantum formalism are a matter of ongoing debate. Indeed, time appears to be merely a parameter (c-number) but of course dynamical variables of specific quantum systems (clocks) may be used as substitutes of time. In 1933, Pauli gave a famous argument on the impossibility of introducing a universal time operator Tu obeying the canonical commutation relation [Tu, H ] = ih̄ for any Hamiltonian. According to Pauli, 3