Operator relation among neutrino fields and oscillation formulas in   matter
  Starting with the relation between two kinds of neutrino field operators corresponding to definite flavor and mass states, we investigate if the usual evolution relations for neutrino oscillation in matter can be consistently derived, in the case of high energy neutrinos. A negative answer is obtained contrary to an earlier result [P. D. Mannheim, Phys. Rev. D {\bf 37} (1988) 1935]. The reason for such a difference relies essentially on the Bogolyubov transformation between two kinds of momentum-helicity creation- and annihilation-operators with definite flavors and masses, which was not taken into account in previous treatments. 
Kanji Fujii, Chikage Habe, Massimo Blasone