Relativistic wave packets in the quantum field approach to the theory of neutrino oscillations

A covariant theory of wave packets and its application to the quantum field method of calculation of the probabilities of neutrino oscillations in vacuum that is based on the technique of macroscopic Feynman diagrams, which describe the processes of emission and absorption of virtual massive neutrinos ν _i (i = 1, 2, 3) at macroscopicly separated space-time points, is considered. The effect of flavor oscillations is reduced to an interference of amplitudes with different vi in an intermediate state. A macroscopic amplitude is calculated that describes a class of processes which go with nonconservation of leptonic numbers, and statistical averaging of the squared modulus of this amplitude is performed. The averaged probability of a process with ultrarelativistic neutrino exchange is representable in the form of an integral of the product of three factors: the flux of massless neutrinos from the source, the differential cross-section for the interaction of a neutrino with the detector, and a dimensionless factor that describes the flavor transition. The conditions under which the last factor can be interpreted as the probability of the flavor transition in the conventional quantummechanical sense are analyzed.