2024/05/07 by Kazuo Fujikawa, Fujikawa, Kazuo
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Neutrino Physics Research
paper · pdf · doi:10.48550/arxiv.2405.03940
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The oscillations of ultra-relativistic neutrinos are realized by the propagation of assumed zero-mass on-shell neutrinos with the speed of light in vacuum combined with the phase modulation by the small mass term exp[-i(m2_νk/2|p|)τ] with a time parameter τ. This picture is realized in the first quantization by the mass expansion and in field theory by the use of δ(x0-y0-τ) ⟨ 0|T⋆νL k(x)νL k(y)|0⟩ with the neutrino mass eigenstates νL k and a finite positive τ after the contour integral of the propagating neutrino energies. By noting that the conventional detectors are insensitive to neutrino masses, the measured energy-momenta of the initial and final states with assumed zero-mass neutrinos are conserved. The propagating neutrinos preserve the three-momentum in this sense but the energies of the massive neutrinos are conserved up to uncertainty relations and thus leading to oscillations. Conceptual complications in the case of Majorana neutrinos due to the charge conjugation in d=4 are also discussed.