Flavor oscillations by itself and its coupling with chiral oscillations and/or spin-flipping are the most relevant quantum phenomena of neutrino physics. This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first quantization and second quantization theories. At first, the basic controversies regarding quantum-mechanical derivations of the flavor conversion formulas are reviewed based on the internal wave packet (IWP) framework. In this scenario, the use of the Dirac equation is required for a satisfactory evolution of fermionic mass-eigenstates since in the standard treatment of oscillations the mass-eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. Within first quantized theories, besides flavor oscillations, chiral oscillations automatically appear when we set the dynamic equations for a fermionic Dirac-type particle. It is also observed that there is no constraint between chiral oscillations, when it takes place in vacuum, and the process of spin-flipping related to the helicity quantum number, which does not take place in vacuum. The left-handed chiral nature of created and detected neutrinos can be implemented in the first quantized Dirac theory in presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. These modifications introduce correction factors proportional to m(v)(2)/E-v(2) that are very difficult to be quantified by the current phenomenological analysis. All these effects can also be identified when the non-minimal coupling with an external (electro) magnetic field in the neutrino interacting Lagrangian is taken into account. In the context of a causal relativistic theory of a free particle, one of the two effects should be present in flavor oscillations: (a) rapid oscillations or (b) initial flavor violation. Concerning second quantized approaches, a simple second quantized treatment exhibits a tiny but inevitable initial flavor violation without the possibility of rapid oscillations. Such effect is a consequence of an intrinsically indefinite but approximately well defined neutrino flavor. Within a realistic calculation in pion decay, including the quantum field treatment of the creation process with finite decay width, it is possible to quantify such violation. The violation effects are shown to be much larger than loop induced lepton flavor violation processes, already present in the standard model in the presence of massive neutrinos with mixing. For the implicitly assumed fermionic nature of the Dirac theory, the conclusions of this report lead to lessons concerning flavor mixing, chiral oscillations, interference between positive and negative frequency components of Dirac equation solutions, and the field formulation of quantum oscillations. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
