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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 coherent state that corresponds to the homogeneous condensate, the quantum depletion of the expectation value of the field-operator is demonstrated to be due to the annihilation of the condensate constituents into relativistic quanta. Moreover, due to the fact that the initial field acceleration and energy for the non-squeezed coherent states are determined in terms of bare coupling constant, instead of the renormalized one, the appearance of perturbative singularities is shown to be inevitable. In other words, consistency of these states requires the finiteness of the bare coupling constant, through the resummation.