Classical analog of the T. D. Lee model for renormalization

TL;DR

This paper demonstrates a classical analog of the quantum Lee model using coupled harmonic oscillators, revealing that classical frequency divergence and renormalization mirror quantum mass divergence and scattering behaviors, challenging the quantum-centric view.

Contribution

It introduces a classical model that replicates quantum renormalization phenomena, providing new insights into classical-quantum correspondence in renormalization theories.

Findings

Classical frequency divergence parallels quantum mass divergence.

Renormalization conditions are established for classical coupled oscillators.

Classical scattering dependence on cutoff mirrors quantum behavior.

Abstract

While divergence and renormalization of physical quantities are frequently encountered in quantum field theory (QFT), they are not necessarily quantum-specific characteristics. We show in this paper that there exists a classical counterpart of the Lee model which is the model of coupled harmonic oscillators (CHO). It is demonstrated that the frequency divergence in this classical model precisely replicates the phenomenon of mass divergence in the Lee model, as does the corresponding renormalization procedure. Considering the arbitrariness in renormalization schemes, we establish necessary conditions that a general renormalization must satisfy for the model of two coupled oscillators which corresponds to the single-mode Lee model. Furthermore, we analyze the classical analog of $N\text{-}\theta$ scattering process and show that the dependence of scattering strength on the cutoff mode mirrors that of the quantum case. These findings challenge the quantum-centric view of mass renormalization in the Lee model and offer new insights into the classical-quantum correspondence in renormalization theories.