Tools of quantum information theory can be exploited to provide a convenient description of the phenomena of particle mixing and flavor oscillations in terms of entanglement, a fundamental quantum resource. We extend such a picture to the domain of quantum field theory where, due to the nontrivial nature of flavor neutrino states, the presence of antiparticles provides additional contributions to flavor entanglement. We use a suitable entanglement measure, the concurrence, that allows extracting the two-mode (flavor) entanglement from the full multimode, multiparticle flavor neutrino states.
Recent work on neutrino oscillations suggests that the three generations of fermions in the standard model are related by representations of the finite group A(4), the group of symmetries of the tetrahedron. Motivated by this, we explore models which extend the EPRL model for quantum gravity by coupling it to a bosonic quantum field of representations of A(4). This coupling is possible because the representation category of A(4) is a module category over the representation categories used to construct the EPRL model. The vertex operators which interchange vacua in the resulting quantum field theory reproduce the bosons and fermions of the standard model, up to issues of symmetry breaking which we do not resolve. We are led to the hypothesis that physical particles in nature represent vacuum changing operators on a sea of invisible excitations which are only observable in the A(4) representation labels which govern the horizontal symmetry revealed in neutrino oscillations. The quantum field theory of the A(4) representations is just the dual model on the extended lattice of the Lie group E6, as explained by the quantum McKay correspondence of Frenkel, Jing and Wang. The coupled model can be thought of as string field theory, but propagating on a discretized quantum spacetime rather than a classical manifold.
We consider a class of models for the relativistic covariant wave packets (WPs) which can be used as asymptotically free in and out states in the quantum field theoretical formalisms for description of the neutrino flavor oscillation phenomenon. We demonstrate that the new “asymmetric” wave packet (AWP) is an appropriate alternative to the more conventional “symmetric” WPs, like the so-called relativistic Gaussian packet (RGP) widely used in the quantum field theory (QFT)-based approaches to neutrino oscillations. We show that RGP is not a particular case of AWP, although many properties of these models are almost identical in the quasistable regime. We discuss some features of AWP distinguishing it from RGP.
Neutrino oscillations: quantum mechanics vs. quantum field theory
