Stanisław D. Głazek, Arkadiusz P. Trawiński
Neutrino oscillations are described and interpreted using the front form of Hamiltonian dynamics in the Feynman--Gell-Mann--Levy version of an effective quantum field theory in which leptons interact with whole nucleons and pions instead of quarks. The interactions are treated in the lowest-order perturbative expansion in the coupling constants in the effective theory, including a perturbative solution of the coupled constraint equations. Despite missing quarks and their binding mechanism, the effective Hamiltonian description is sufficiently precise for showing that the standard oscillation formula results from the interference of amplitudes with different neutrinos in virtual intermediate states. This holds provided that the inherent experimental uncertainties of preparing beams of incoming and measuring rates of production of outgoing particles are large enough for all of the different neutrino intermediate states to contribute as alternative virtual paths through which the long-base scattering process can manifest itself. The front-form result is the same as the previously derived instant-form result despite that the long-base scattering process is traced in space-time differently and the relevant interaction Hamiltonians are constructed differently in the different forms of dynamics.
View original:
http://arxiv.org/abs/1208.5255
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