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A consistent constructive covariant description of neutrino flavourtransition amplitude in vacuum is presented. To this end a special generalizedrelativistic wave packet is constructed with correct extension onto the higherspins. This packet is uniquely defined as an `interpolating' wave packet, whichby means of relativistically invariant `width' accurately interpolates betweenthe states localized in momentum space and in coordinate space. The wave packetis unambiguously determined by analytical properties of Wightman functions incomplex coordinate space naturally connected with its minimization properties.The packet gives natural relativistic generalization of non relativisticGaussian wave packet but it contains covariant states of particle(antiparticle) only with positive (negative) energy sign and propagates withouttheir mixing and without changing of its relativistically invariant width. Forthe diagrammatic treatment of oscillation with the use of these wave packetsfor external particles, the notion of covariant composite wave function forintermediate neutrino is introduced. It strictly and naturally connects bothoscillation pictures, giving an effective language for detailed description ofthis process, and resolves the problems with causality and with covariant equaltime prescription for the intermediate neutrino picture. It is closely relatedto overlap function of neutrino creation/detection vertices, elucidating acovariant meaning of the `pole integration' procedure. Their space-timeasymptotic behaviour in narrow-packets approximation naturally conforms withsuch approximation of one-packet state and with the asymptotic behaviour ofoscillation amplitude. The respective overlap function is explicitly calculatedfor two-packet example of pion decay vertex. Its correspondence and differencewith previous approximate calculations is analyzed.

Interpolating wave packets and composite wave functions in QFT and neutrino oscillation problem