Neutrino mixing and oscillations in quantum field theory: a comprehensive introduction.

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrate some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exist entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which imposes a lower bound on the precision of neutrino energy measurements and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.