Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 39

There exists a choice of basis in which all Dirac matrices are purely imaginary. This is called the Majorana representation of the Gamma-matrices. They are obtained from the corresponding ones in the Dirac representation via the unitary transformation

with

and have the property

One explicitly computes

Now, the Dirac wave function and its charge conjugate (in the Dirac and Weyl representations) are related by (see Chapter 7, Eq. (7.48)),

Applying the unitary operator (4.65) to both sides of the equation, we obtain for the Dirac wave function in the Majorana representation

where

We thus conclude that

Summarizing we have in the Dirac, Weyl and Majorana representations

where