Alternative Fock quantization of neutrinos in flat space-time

Abstract

The neutrino equations in flat space-time are studied in static Rindler accelerated coordinates and in the Penrose conformal coordinates. It is found that the definition of a positive frequency solution to the Dirac equation in the Rindler coordinates is not equivalent to that in Minkowski coordinates, implying inequivalent Fock representations in the two coordinate systems. The definition of positive frequency in the Penrose conformal metric is found to be exactly equivalent to that of Minkowski spacetime. A complete set of solutions is found, and the ‘energy' spectrum is discrete ( ω = 2 n + 1, n > j , where j is the total angular momentum of the eigenfunction) and excludes zero frequency.