When the time evolution of the coherent-state wavefunction is considered and the properties of the coherent states are exploited, one should take into account the properly defined phase factor. After discussing this point, we derive the expression for the required phase and correct some errors occurring in the literature.
The idea that the phase of single-mode field may be correctly defined as a phase difference between the state considered and a highly excited coherent state treated as the reference phase state, although present in discussions about the quantum phase problem, have not been directly concretized and its consequences fully understood. In the present work we succeed in finding an effective mathematical procedure which corresponds exactly to this idea and so derive, using the results related to phase difference available in the literature, the phase distribution for a single-mode field. We discuss the obtained results.
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the $\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\ensuremath{-}N$ evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N1/2.
We consider the time evolution of order parameter correlation functions after a sudden quantum quench of the magnetic field in the transverse field Ising chain. Using two novel methods based on determinants and form factor sums respectively, we derive analytic expressions for the asymptotic behaviour of one- and two-point correlators. We discuss quenches within the ordered and disordered phases as well as quenches between the phases and to the quantum critical point. We give detailed accounts of both methods.