Field theory description of neutrino oscillations

Abstract

We review various field theory approaches to the description of neutrino oscillations in vacuum and external fields. First we discuss a relativistic quantum mechanics based approach which involves the temporal evolution of massive neutrinos. To describe the dynamics of the neutrinos system we use exact solutions of wave equations in presence of an external field. It allows one to exactly take into account both the characteristics of neutrinos and the properties of an external field. In particular, we examine flavor oscillations an vacuum and in background matter as well as spin flavor oscillations in matter under the influence of an external electromagnetic field. Moreover we consider the situation of hypothetical nonstandard neutrino interactions with background fermions. In the case of ultrarelativistic particles we reproduce an effective Hamiltonian which is used in the standard quantum mechanical approach for the description of neutrino oscillations. The corrections to the quantum mechanical Hamiltonian are also discussed. Note that within the relativistic quantum mechanics method one can study the evolution of both Dirac and Majorana neutrinos. We also consider several applications of this formalism to the description of oscillations of astrophysical neutrinos emitted by a supernova and compare the behavior of Dirac and Majorana neutrinos. Then we study a spatial evolution of mixed massive neutrinos emitted by classical sources. This method seems to be more realistic since it predicts neutrino oscillations in space. Besides oscillations among different neutrino flavors, we also study transitions between particle and antiparticle states. Finally we use the quantum field theory method, which involves virtual neutrinos propagating between production and detection points, to describe particle-antiparticle transitions of Majorana neutrinos in presence of background matter.

Parity violation and chiral oscillation of cosmological relic neutrinos

“…With these taken into consideration, the Majorana condition, ν c M (t) = ν M (t), holds for chiral oscillation at an arbitrary time. Valuable discussions can be found in [26][27][28][29].…”

Canonical Quantization of a Massive Weyl Field

“…Ref. [15], one may choose a non-singular weight coefficient like in the book by Fukugita & Yanagida [8].…”

“…In the classical field theory [15], the expansion coefficients a ± (p) and b ± (p) were supposed to be c-number functions. However now we assume that these objects are commuting or anticommuting operators.…”

“…Nevertheless the results of our work can be easily generalized to include several neutrino generations. Note that the evolution of mixed massive Dirac and Majorana neutrinos was studied in frames of the relativistic quantum mechanics (or classical field theory) to phenomenologically describe neutrino oscillations in vacuum and various external fields (see the review by Dvornikov [15] and references therein).…”

On some developments in the Nonsymmetric Kaluza-Klein Theory

“…and ζ = ±1 describes different polarization states of the fermions Ψ a (see Refs [54], [55]). In our case E(+)…”