Y. F. Perez, C. J. Quimbay
The main goal of this work is to perform an introduction to the Majorana's
formalism of neutrino oscillations and to study its physical consequences. To
do it we calculate the probability amplitude of transition in vacuum between
two neutrino flavor states by considering neutrinos as Majorana fermions. We
perform this calculation in the context of an approach developed in the
canonical formalism of Quantum Field Theory for the case of the propagation of
neutrinos which are considered as superpositions of mass-eigenstate plane waves
with specific momenta. First we obtain and solve the two-component Majorana
equation and then we develop the canonical quantization procedure for the
Majorana field. Next we calculate the probability amplitude of transition
between two different neutrino flavor states. In the same approach and by
establishing normalization and boundary conditions we can obtain the Majorana
neutrino oscillations for two cases: the ultra-relativistic and
non-relativistic limits. While the first case for neutrino oscillations is well
known in the literature, the second one is phenomenologically restricted as is
shown when the propagation of heavy neutrinos is considered as superpositions
of mass-eigenstate wave packets.
View original:
http://arxiv.org/abs/1103.2781
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