Symmetries in neutrino-electron scattering

The symmetries of the neutrino-electron scattering kernel are exposed. The kernel must explicitly conserve particle number at each vertex and vanish in local thermodynamic equilibrium. I show that the latter requirement must be met by the combination of detailed balance between in and out beams and a symmetry property of the kernel that until now has gone unnoticed. Exploitation of this extra symmetry approximately doubles the computational efficiency of the algorithm.