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arXiv · 1507.01256

Particle quantum states with indefinite mass and neutrino oscillations

A. E. Lobanov
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Abstract

In this work we develop a mathematical formalism which allows obtaining oscillation formula for neutrino of any energy. We demonstrate that in the ultra-relativistic limit the results obtained in this new approach agree with the previously used phenomenological theory which is only applicable to ultra-relativistic neutrinos. To this end we do the following. The Hilbert spaces of particle states are constructed in such a way that the neutrinos are combined in a multiplet with its components being considered as different quantum states of a single particle. The same is done for the charged leptons and the down- and up-type quarks. In the theory based on the Lagrangian of the fermion sector of the Standard Model modified in accordance with this construction, the phenomenon of neutrino oscillations arises as a direct consequence of the general principles of quantum field theory. Using the example of the pion decay, when the resulting neutrino has to be ultra-relativistic, it is shown that the neutrino states produced in the decay process can be described by a superposition of states with different masses and identical canonical momenta with very high accuracy.

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A. E. Lobanov. 2019-06-27. Particle quantum states with indefinite mass and neutrino oscillations. https://doi.org/10.1016/j.aop.2019.02.001

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