A New Approach to Canonical Quantization of the Radiation Damping

TL;DR

This paper introduces a novel canonical quantization method for radiation damping by formulating a Lagrangian with a Chern-Simons-like term and performing Hamiltonian analysis, advancing the understanding of dissipative quantum systems.

Contribution

It presents a new approach to quantizing radiation damping using an indirect Lagrangian with a Chern-Simons-like term and Hamiltonian formalism, extending previous dissipative system quantizations.

Findings

Derived a Lagrangian with Chern-Simons-like term for radiation damping

Performed Hamiltonian analysis leading to quantization

Provides a new framework for dissipative quantum systems

Abstract

Inspired in some works about quantization of dissipative systems, in particular of the damped harmonic oscillator\cite{MB,RB,12}, we consider the dissipative system of a charge interacting with its own radiation, which originates the radiation damping (RD). Using the indirect Lagrangian representation we obtained a Lagrangian formalism with a Chern-Simons-like term. A Hamiltonian analysis is also done, what leads to the quantization of the system.