ABSTRACT
We have seen that Dirac spinors transform according to a reducible representation of the Lorentz transformations. On the basis of transformations of https://www.w3.org/1998/Math/MathML" display="inline"> L + ↑ https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003436263/11a1814b-c2ab-4d89-be15-80efb520b7b3/content/math13_1.tif"/> only it should therefore be possible to find smaller, truly irreducible representations to describe a spin https://www.w3.org/1998/Math/MathML" display="inline"> 1 2 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003436263/11a1814b-c2ab-4d89-be15-80efb520b7b3/content/math13_2.tif"/> particle. This reduction leads to two types of theory, of the Weyl neutrino and the Majorana neutrino.
