Classical Radiation Damping and Emission of Optical Vertex as Microscopic Irreversible Process

Radiation damping process by a charged particle in classical dynamics is discussed in terms of a complex spectral analysis of the Liouville operator in an extended function space outside the Hilbert space. The complex spectral analysis has been introduced to describe irreversible process with a broken time-symmetry on a rigorous dynamical basis starting from the fundamental laws of physics. Thanks to this analysis, we show that the long-standing difficulty of that leads to non-dynamical behaviors such as non-causal behavior and the existence of a runaway solution of the charged particle has been resolve. The propagation of the optical vertex inside a waveguide is also discussed.