Towards neutrino transport with flavor mixing in supernovae: the Liouville operator

TL;DR

This paper develops a formalism for neutrino transport in supernovae that incorporates both collisions and flavor mixing by constructing distribution matrices and deriving Liouville equations for neutrinos and antineutrinos.

Contribution

It introduces a framework for neutrino and antineutrino distribution matrices and derives their Liouville equations, advancing the modeling of neutrino flavor mixing in supernova environments.

Findings

Constructed neutrino and antineutrino distribution matrices.

Derived Liouville equations for these matrices in the noninteracting case.

Laid groundwork for including flavor mixing in neutrino transport models.

Abstract

The calculation of neutrino decoupling from nuclear matter requires a transport formalism capable of handling both collisions and flavor mixing. The first steps towards such a formalism are the construction of neutrino and antineutrino "distribution matrices," and a determination of the Liouville equations they satisfy in the noninteracting case. These steps are accomplished through study of a Wigner-transformed "density function," the mean value of paired neutrino quantum field operators.