On Evolution of Coherent States as Quantum Counterpart of Classical Dynamics

Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the interaction-picture formalism. One of the important aspects of our analysis consists in utilizing the operators and the vacuum of interacting theory in constructing the states, without invoking asymptotic particles. Focusing on a coherent state describing a spatially homogeneous field configuration, it is demonstrated that both adopted methods successfully account for nonlinear classical dynamics, giving distinguishable quantum effects. In particular, according to the time-expansion analysis the initial field-acceleration, with which the field departs from its initial expectation value, is governed by the tree-level potential with renormalized mass and bare coupling constant. The interaction-picture computation, instead, can be manipulated to give the nonlinear dynamics, determined in terms of renormalized coupling and mass. However, it results in a logarithmic initial-time singularity in the field-acceleration, reminiscent of the similar behaviour encountered within semi-classical formalism, for certain choices of the initial state for fluctuations. Within our coherent-state analysis, the above mentioned peculiarities are artefacts of an expansion: in the first case over infinitesimal time, while in the second case in the coupling constant. Despite this, we show that the evolution obtained within the interaction-picture analysis is valid for extended period of time. Moreover, on top of the desired classical dynamics, it serves us with interesting quantum corrections, previously proposed by Dvali-Gomez-Zell.