Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 38

So far we have considered the Dirac representation, particularly suited for discussing the non-relativistic limit as we shall see, and the Weyl (or chiral) representation particularly suited for discussing the relativistic limit, or the case of zero mass particles. There exists another choice of basis for the Gamma matrices called the Majorana representation which is particularly suited for the case of charge self-conjugate fermions, referred to as Majorana fermions.

Spin zero, charge neutral particles are called “self-conjugate”, and are described by real fields satisfying the Klein–Gordon equation, which itself is real. In the case of “self-conjugate” spin one-half particles, the analogon is provided by the “Majorana” representation.

The Majorana representation is, however, also useful in the case where fermions and anti-fermions are distinct particles if the symmetry group in question is for instance the orthogonal group O(N) rather than the unitary group U(N). The reason is that in the Majorana representation the Dirac equation is real. We therefore discuss separately the notion of Majorana representation and Majorana fermions.