Non-Abelian gauge structure and flavor mixing in quantum field theory¹

Abstract

The quantum field theory formalism describing the phenomenon of neutrino mixing and oscillations is reviewed in its essential aspects. The condensate structure of the flavor vacuum state is considered and its non-perturbative nature is discussed within the existence in the quantum field theory of the manifold of unitarily inequivalent representations of the anticommutation relations. The Poincaré structure of the theory is discussed in connection with the gauge theory features of neutrino mixing, where the possibility arises to describe flavored neutrinos as on-shell fields with definite masses. The flavor vacuum state may be thought of as a refractive medium where different refraction indexes are related to the different neutrino masses. Neglecting the condensate structure of the flavor vacuum implies neglecting second-order contributions in the gauge field coupling and leads to experimentally inconsistent results.

Neutrino Oscillations in Finite Time Path Out-of-Equilibrium Thermal Field Theory

“…The variety of extant approaches includes the Majorana mass term, right-handed neutrinos with a see-saw mechanism, supersymmetric extensions of Standard model, and more. One intriguing possibility is the generation of neutrino masses and mixing via the aforementioned flavor vacuum condensate [46][47][48]. However, in the present paper we do not address the issue of the origin of neutrino masses, and focus on demonstrating the calculation of neutrino oscillations in the FTPFT framework.…”

“…Nevertheless, we adopt the approximation where the neutrino mixing is fully due to the term L Mix , that is, we neglect the residual influence of L W on the neutrino masses and mixing. Of course, we must keep in mind the caveat that not calculating these corrections misses the contributions from the vacuum condensate, which Blasone et al [46][47][48] found to be important corrections to the PMNS result. Nevertheless, they vanish in the relativistic limit, while the PMNS result is recovered [46][47][48].…”

“…Of course, we must keep in mind the caveat that not calculating these corrections misses the contributions from the vacuum condensate, which Blasone et al [46][47][48] found to be important corrections to the PMNS result. Nevertheless, they vanish in the relativistic limit, while the PMNS result is recovered [46][47][48]. Because the case of nonrelativistic neutrino kinematics seems to be far from present experimental capabilities, we proceed to study neutrino propagators in our aforedescribed framework, which provides us with an exactly solvable model suitable for studying how FTPFT can be applied to neutrino oscillations.…”