Transport Theory of Massless Fields

TL;DR

This paper derives transport equations for massless quantum fields using the Schwinger-Keldysh technique, revealing how interactions induce quasiparticle masses and modify kinetic equations, with differences between $$ and $$ models.

Contribution

It provides a detailed derivation of transport equations for massless fields, highlighting the emergence of quasiparticles in the  model and the absence of such in the  model, including new terms beyond standard Boltzmann equations.

Findings

Quasiparticles emerge in the  model due to self-interaction.

Finite width quasiparticles are described by modified kinetic equations.

The  model does not support quasiparticle transport theory.

Abstract

Using the Schwinger-Keldysh technique we discuss how to derive the transport equations for the system of massless quantum fields. We analyse the scalar field models with quartic and cubic interaction terms. In the $\phi^4$ model the massive quasiparticles appear due to the self-interaction of massless bare fields. Therefore, the derivation of the transport equations strongly resembles that one of the massive fields, but the subset of diagrams which provide the quasiparticle mass has to be resummed. The kinetic equation for the finite width quasiparticles is found, where, except the mean-field and collision terms, there are terms which are absent in the standard Boltzmann equation. The structure of these terms is discussed. In the massless $\phi^3$ model the massive quasiparticles do not emerge and presumably there is no transport theory corresponding to this model. It is not surprising since the $\phi^3$ model is anyhow ill defined.