Background-field method and initial-time singularity for coherent states

The background-field method is adopted for studying the dynamics of coherent states within an interacting scalar field theory. Focusing on a state that corresponds to homogeneous condensate, quantum depletion expectation value operator demonstrated be due annihilation condensate constituents into relativistic quanta. Moreover, fact initial acceleration and energy nonsqueezed are determined in terms bare coupling constant, instead renormalized one, appearance perturbative singularities shown inevitable. In other words, consistency these requires finiteness through resummation.