ABSTRACT
Neutrinos as fundamental leptons are spin-12 particles like other fermions; however, it is an experimental fact that only left-handed neutrinos and right-handed antineutrinos are observed. In quantum field theory spin-12 particles are described by four-component wavefunctions (spinors) which obey the Dirac equation. The Dirac mass term can be written in its chiral components (Weyl spinors). Applying this to neutrinos, it requires both a left- and a right-handed Dirac neutrino to produce such a mass term. In the Standard Model of particle physics only left-handed neutrinos exist; this is the reason why neutrinos remain massless. Conserved quantum numbers arise from the invariance of the equation of motion under certain symmetry transformations. Continuous symmetries (e.g., translation) can be described by real numbers and lead to additive quantum numbers, while discrete symmetries (e.g., spatial reflections through the origin) are described by integers and lead to multiplicative quantum numbers.
