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

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.