Higher-Order Approximation of Coherent State Dynamics in Self-Interacting Quantum Field Theories

TL;DR

This paper develops a detailed higher-order approximation method for the evolution of coherent states in self-interacting quantum field theories, extending previous leading-order results to arbitrary order.

Contribution

It introduces a systematic asymptotic expansion for quantum evolution in self-interacting bosonic fields, including non-polynomial interactions, refining earlier leading-order analyses.

Findings

Constructed asymptotic expansion of quantum evolution for coherent states.

Extended results from polynomial to non-polynomial interactions.

Provided rigorous analysis under standard assumptions for self-adjointness and well-posedness.

Abstract

We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field dynamics, non-linear and linear respectively, we construct an asymptotic expansion of arbitrary order for the quantum evolution of coherent states. The results are first established for the spatially cutoff $P({\phi})_2$ model, under standard assumptions ensuring essential self-adjointness of the Hamiltonian and well-posedness of the classical flow, and are then extended to a class of non-polynomial analytic interactions. This work refines and generalizes earlier results, which identified only the leading-order term of the expansion.