Abstract
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 giving 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 illustrates 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 exists 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 impose 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.
Highlights
Neutrinos are described by quantum fields, and their proper treatment requires the formalism of quantum field theory (QFT), and in particular of those features that make
The use of the flavor vacuum allows to define the exact eigenstates of the flavor charges, and an exact oscillation formula can be derived by taking the expectation values of flavor charges on flavor states
Section 7), i.e., a form of Mandelstam–Tamm uncertainty relation involving flavor charges, which fixes a lower bound on neutrino energy resolution
Summary
The study of neutrino mixing and oscillations has attracted much attention in past decades and the present day in the theoretical [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] and experimental [21,22,23,24,25] research activity. Under proper boundary conditions, different dynamical regimes may exist, i.e., different phases of the system, each one described by a different (unitary non-equivalent) representation The discovery of such a structural aspect of QFT, in the early 1950s of the past century, after a first “disappointment”, was recognized to be the great richness of QFT [31,32,33,34,35]. The unique possibility offered by QFT of defining the flavor vacuum permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges, showing its physical significance This leads, in turn, to the exact oscillation formula, which differs from the one obtained in the QM approximation [7]. In Appendix C, by using the first quantization methods applied to the Dirac equation, which do not explicitly exhibit the foliation into the QFT unitarily inequivalent representations, it is obtained that the oscillation formula is consistent with the one derived in the QFT formalism
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
