Background Field Method and Initial-Time Singularity for Coherent States

TL;DR

This paper uses the background field method to analyze the dynamics of coherent states in an interacting scalar field theory, revealing initial-time singularities linked to the bare coupling constant and quantum depletion mechanisms.

Contribution

It demonstrates the quantum depletion process of coherent states and shows that initial-time singularities arise due to the use of bare coupling constants, requiring resummation for consistency.

Findings

Quantum depletion results from condensate annihilation into relativistic quanta.

Initial-time singularities are inevitable when using bare coupling constants.

Resummation is necessary to ensure the finiteness of the theory.

Abstract

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.