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

• We investigate a classical model of coupled harmonic oscillators (CHO) as the classical counterpart of the Lee model. In this classical model, the divergence of the fundamental frequency and its renormalization precisely reproduce the divergence and renormalization of the physical mass of the particle, revealing that mass divergence in the Lee model is not solely a quantum phenomenon. • We derive the necessary conditions that any renormalization must satisfy for the two-oscillator system corresponding to the single-mode Lee model. • We examine the classical analog of the N - θ scattering process in the Lee model and demonstrate that the cutoff-dependent behavior of the scattering strength parallels the quantum scenario, indicating that the suppression of scattering also has a classical origin. Although 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 the N - θ 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.